You might as well just use him for TT to collect some feathers from hero merit and also enjoy him being actually strong even without investment. After that you can just bench him indefinitely. He works well with refined nameless blade + LnD, but it's not really worth the investment in your case.
So my free summon on the TT banner was a neutral Karel but I'm not sure what to do with him as I feel he'll likely just collect dust on my bench?
My main merge project is Fir who's at +5 and already has the refined Nameless Blade. I have +spd/-hp +2 Lucina, +atk/-spd Lyn, and +atk/-res Leif so it feels like I don't really need another infantry sword. And even then I have a 4* +spd/-def Soleil who'd probably be a better option should I eventually promote her.
When it comes to the TT, I already had plans to SP grind SF!Nino a bunch with it. I do have a shortage of Shannas and units like SF!Nino, Ishtar, Caeda, and Micaiah all stuck with Desp 2 currently, although Micaiah swaps between it and QR depending on if I need a more offensive or defensive build. But it feels almost too wasteful to fodder only to give one of them just Desp 3. Maybe I could make it so Leif gets both Wo Dao+ and Desp 3?
I pretty much co-sign what everybody else said - good Wo Dao and Desperation fodder if you need it.
I'll play devil's advocate and say that his HP makes him a good Infantry Pulse user, and since IP stacks, you can make some creative team comps around it or utilize that in some AA teams. Also if you're working on Fir, you could always make a theme team with Fir, Karel, Karla, and Bartre lol.
You could also make him a niche AA units with Triangle Adept and a breaker skill. Less general than Fir but useable in certain cases.
The thing with Infantry Pulse is my only unit with it is 5*+1 Marisa and I'd rather not fodder her off. Especially when given that my Karel is neutral his only stat better than her is hp, by 1, but even that is offset by the merge.
And unfortunately I can't see myself trying that theme team anytime soon, no Karla but even if I got her I'd be very tempted to give Fir Wrath. And two Fir is by far my favorite Binding Blade character and one of my favorite swordmasters in the series, hence the merge project, but I don't have that same main series attachment to the rest of her family.
I got him for free in one of the previous banners, and I find Trials to be a good motive to pick him up. I'll likely be running him with Fury, Desperation + Speed Seal & Moonbow with Nameless Blade. Pretty cheap and likely to be killing most Non-Blues (especially with Trials bonus stats).
He's also a bonus unit, so there's that.
I'd be more motivated to use him in TT if I didn't already have SF!Nino, and want to give her more SP and HM through the TT. And she then frees up space to use a different sword unit like Ares, who was pretty fun in the last TT given how he'll likely be firing off specials constantly after the first map.
If you grind the TT religiously, you’re going to max out SF Nino on HM and SP pretty quickly. Having Karel along for the ride could help you keep a fresh bonus unit and still rack up HM quickly, unless you already have multiple bonus units you plan to grind. I know last TT I maxed out Groom Marth and nearly maxed out OG Marth while scoring over 300K. If you don’t grind that much, then you can probably kill Karel right now along with a 4* Mae so you have the option of getting both desperation 3 and wo dao+.