The thing is, “thanks for your concern” is a stock phrase that probably would have read as sincere at some point in the middle of the last century, but it’s been so solidified as a cliché implying insincerity and condescension that it’s hard not to read that into it now. Saying roughly the same thing with different words would make it easier to read the sentiment as serious instead of sarcastic or condescending — for instance, “thanks for the suggestion” or “thanks for the idea” or “I understand the concern”. It’s not that the individual words wouldn’t add up to say what you mean, it’s that the whole phrase “thank you for your concern” has taken on a specialized use that eclipses the meaning of the individual words.

(For another example, if somebody writes “I didn’t manage to do this last time I tried, but after all the practicing I’ve been doing I’m sure this time is going to work,” you can reply either “Yeah!” or “Right!” and they’ll know you’re agreeing with them, but if you type ”Yeah, right!” that’ll probably be taken as sarcastic.)