If you take a closer look at the popular decks here on Arkhamdb, you may notice that still most of them use a complete set of Guts, Perception, Overpower and Manual Dexterity. I omit Unexpected Courage here, because it functions a bit different.

These cards' popularity is based on their marginal cost and the high versatility they give you. Each of them occupies one deck slot, but there is (on Standard difficulty) a huge chance of drawing another card, so it feels as if they cost nothing. They kind of "replace themselves instantly". Whatever strategy you are running, tests over all four attributes will meet you at every corner (or in every Mythos phase) and you don't have to commit these skills to a particular kind of skill test. The above-mentioned reasons, as a sum, virtually "reduce" your deck size and enable you to draw your key cards much faster. In fact, playing them includes two slight risks:

• The test can fail and the skill does not replace itself.
• The skill succeeeds and the card you draw is your Weakness. Especially, this risk can hurt if you Weakness happens to be Amnesia.

Pros

• +2 on a test for (almost) no tempo hit is really, really good. If taking the test costs you an action, and you're even on the difficulty, then the resulting tempo bump is, on average, worth almost an entire action.
• Can be committed to another player's skill test.
• Zero play cost
• Card text has no trigger restriction (as in Vicious Blow e.g.)
• Combines perfectly with cards that have an additional effect if you overfulfill: List
• "Ashcan" Pete gets more value out of the skill card than the other investigators, since the extra card you draw also works as smelling salts to wake his dog up.
• On High/Expert difficulty you do not want to fail on skill tests, so the +2 bonus alone justifies the inclusion.

Cons

• "Max 1 committed per skill test" across all players.
• The skill succeeeds and the card you draw is a Weakness.

If you take a closer look at the popular decks here on Arkhamdb, you may notice that still most of them use a complete set of Guts, Perception, Overpower and Manual Dexterity. I omit Unexpected Courage here, because it functions a bit different.

These cards' popularity is based on their marginal cost and the high versatility they give you. Each of them occupies one deck slot, but there is (on Standard difficulty) a huge chance of drawing another card, so it feels as if they cost nothing. They kind of "replace themselves instantly". Whatever strategy you are running, tests over all four attributes will meet you at every corner (or in every Mythos phase) and you don't have to commit these skills to a particular kind of skill test. The above-mentioned reasons, as a sum, virtually "reduce" your deck size and enable you to draw your key cards much faster. In fact, playing them includes two slight risks:

• The test can fail and the skill does not replace itself.
• The skill succeeeds and the card you draw is your Weakness. Especially, this risk can hurt if you Weakness happens to be Amnesia.

Pros

• +2 on a test for (almost) no tempo hit is really, really good. If taking the test costs you an action, and you're even on the difficulty, then the resulting tempo bump is, on average, worth almost an entire action.
• Can be committed to another player's skill test.
• Zero play cost
• Card text has no trigger restriction (as in Vicious Blow e.g.)
• Combines perfectly with cards that have an additional effect if you overfulfill: List
• "Ashcan" Pete gets more value out of the skill card than the other investigators, since the extra card you draw also works as smelling salts to wake his dog up.
• On High/Expert difficulty you do not want to fail on skill tests, so the +2 bonus alone justifies the inclusion.

Cons

• "Max 1 committed per skill test" across all players.
• The skill succeeeds and the card you draw is a Weakness.

In solo play her ability to foresee the future for relatively cheap makes her damningly powerful. Never again shall the mythos deck contain nasty surprises that you aren't ready for. Hell, sometimes it's even worth losing a turn if the card that threatens to come out is that bad. This effect is easily enough to justify her exorbitant costs, assuming you splurge for some ways to boost your income.

Now I think in multiplayer her role changes slightly. Sure knowing what's coming will help someone in the party survive, but it's a diminishing effect when you're pulling 4 encounter cards a turn. Here I think Alyssa is better served as a guardian angel for particularly time-sensitive weaknesses. Keep Zoey or Roland from pulling their signatures when the clock is running out, or keep watch over the person in your group who has a large pool of resources they're saving for something and a bit of a paranoia streak.

Finally the 'bonuses' of +1 books and a decent sanity body aren't too shabby either. Of course, both of our current Mystics are well equipped to deal with horror, but it doesn't hurt. Plus sometimes you just have to investigate.

Is she better than Skids? No, but she might certainly be worth charisma in solo, or if you're just not the Skids guy in multiplayer she's worth the open ally slot.

This card largely sucks on its own. +3 will can be a butt saver against the encounter deck or critical for pulling off a difficult spell in expert, +3 fight tends to be pretty pointless on Mystics but can help them deal the odd 1 damage (2 with fireaxe or something) but it's definitely not worth losing an equivalent of a whole turn (which is what doom is) for a mediocre boost on either of these stats.

Now the first use case where BP can begin to pull its weight is at the end of an agenda. The additional doom doesn't trigger an agenda-advancement check, and when agendas cycle they remove all doom in play, so if you overload the game board with doom on these turns (with Alyssa Graham and arcane initiate also wanting to use these windows for their doom triggers) it doesn't have any negative effect on the game state. (Watch out for this possibly changing in future scenarios). For scenarios with a lot of agendas this can be really crucial to abuse. Still, it's not the most powerful and its situational that the timing will work out that you need to do these tests before the agenda cycles.

Enter moonlight ritual. Lordy, this is an epic combo. With moonlight you can load up on the doom early in an agenda and clear it before it triggers during the mythos phase. The wonders this works are not to be understated, it is not at all hard to put 6 or 7 doom on Blood Pact early in a long agenda and simply clear it later for a swing of +21 or so in tests for one action and 3exp total. It's bonkers powerful, and fairly consistent since with BP's permanent code word you only need one of your two rituals in hand to have the combo ready.

Now here's the big catch, you need to be hyper aware of what threats are available when doing this. A stray doom or two from the encounter deck, or an unexpected discard effect can have you throwing away 6 turns because of cocky overconfidence. Stay alert for what threats exist and always assume the worst, if you do you too can tap the strength of blood magic without fear of repercussion.

Do you discard all assets in play, as well as cards of the appropriate color in your hand?

The rules about "Ownership and Control" mention: "A player controls the cards located in his or her out-of-play game areas (such as the hand, deck, discard pile)."