IMO this card is almost unrunnable. Between the fact that guardians have very little horror soak and the general fact that these composures are too fragile and the effect not good enough, I honestly don't see any deck that would want this. Compare it to Scrapper (a card that's not even considered to be very good), for 1xp more you could have a permanent one of these. You will miss the 1 horror soak, but it drastically outweighs the problem of having to find and then pay for this card, only for it to discard itself. The one investigator that might actually want this, William Yorick, can use Scrapper, which as I said above is much better.
I find that use is a bit too conditional, but then again so are the new "composure" cards.
The 1 horror shield perk is not terrible but guardians have better ways to shield/prevent/heal horror. The 1 exp cost makes it inferior for this use.
A rich Zoey might benefit from it under certain cicumstances but it's a bit of a head scratcher for Mark and Roland who are not usually resource-plenty. But even with Zoey, and it likely won't survive too long in your play area for you to benefit from it consistently. Mark can use Sophie to buff himself far more reliably and without resource cost.
The fast trait and cheap cost are the evident advantages compared to Physical Training if you're hoping to buff your combat skill. No willpower option however, for which a buff is always handy.
Also, correct me if I'm wrong, assets can only be played during your turn, so you cannot surprise-buff your agility for an encounter card agility test (because when are you buffing your combat during Mythos anyhow?) That means you need to have it played beforehand, adding more to its chances of a premature break.
The slot in your deck is probably better spent on other cards. Likely you'll just commit it than spend two resources to play and trigger.
I'm unconvinced this card is as bad as people are claiming.
The worst way this card could be bad is if you're firmly relying on the fight or evade to make checks at all, and it discards itself. That is a disaster and because it's a disaster this card should not be played in that position.
Where this card has room to be playable is horror soak with the benefit of some turns of turning decent checks into secure ones. At worst, it's the card for a fast resource to horror point. Something Worth Fighting For has the same resource conversion rate, better draw (3 horror for a draw), worse action cost (1/3rd per horror), though is admittedly lvl0. And you're going to have situations where you can simply replace it because you have the other copy in your hand and it doesn't cost an action.
This card would not be too good if it cost zero though (either XP or resources but not both), and would make it considerably more interesting on the deck building side. Honestly, I just think the restriction shouldn't be there. One sanity point on the one composure you can have in play isn't going to break the game without something truly degenerate, and if you're a tough guy, composure isn't the first thing you lose, it's the last thing you lose right before your last sanity point and if that's not thematically appropriate I don't know what is.