“Covering your head while davenin with your tallis is fine as long as that is minhag in that shul or beis medrash. However, to do so in a shul where no one else engages should be done with care so you don’t c’v send the signal that you consider yourself a much more ehrliche yid than others in the tzibur.”
This is true if it’s truly the minhag of that shul that only the Shliach Tzibbur covers his head with a tallis. If you’re talking about going to an MO shul where people happen to not cover there heads with the tallis just because they’re more enlightened than us, then no. There’s a difference between minhagim and societal trends.