The price of 3 is heavy, but I think Trench Coat is a fine card for certain investigators in certain campaigns. I'm a big believer in passive stat boosts. If you build your investigator to evade frequently, you really need effects like this. On Expert, simply relying on the 4 base Agility of the evade-friendly investigators is not going to get results. You need to crank that Agility up somehow. Peter Sylvestre is a great start, but not everyone can take him, and in any case, the more Agility you can stack, the better. Trench Coat will become less a bit less necessary once you get really strong boosts from XP cards like Suggestion or Streetwise.
At the same time, this card is also offering 2 health soak, which is really nice for someone like Sefina. You could compare this card to Holy Rosary. You get a similar amount of value, with a passive stat boost and a soak of 2. Now, Trench Coat is probably worse than the Rosary, since it costs an extra resource and doesn't apply its stat boost all the time. (It does take up a less-contested slot, but this is probably not enough to even things out.) It's a shame that this card doesn't work in the Mythos phase, nor does it synergize with the likes of Backstab. But I think the Rosary is exceptionally strong for a level 0 card, so something a bit worse is not at all unplayable--as long as you're planning on evading a lot.
I especially like Trench Coat in Forgotten Age. First, an evade-focused build is actually good in that campaign. Second, the extra health is very helpful since the campaign is more damage-oriented than any of the others. This card becomes downright essential for Sefina, and even the 7-8 health investigators are going to appreciate it.
Personally, I wouldn't recommend this card for investigators with 3 or fewer Agility (notwithstanding the flavor text). If you're not planning on evading all the time, this card is not very good. There is the health soak, though, and in the Forgotten Age campaign, someone like Akachi or Mateo (who have access to very little health soak otherwise) could consider it for that reason.
To speculate about the future, I'm guessing we'll soon get a level 0 amulet that soaks horror and helps against treacheries, corresponding to Trench Coat in the same way that Elder Sign Amulet corresponds to Bulletproof Vest.