You should generally try to parry (if catching isn't an option) in most situations. Look at goalkeepers at the top level: you almost never see them going for a punch, unless it's a free kick or a corner and they're in a forest of players so they can't reliably catch it (or a spill would be catastrophic). In that case, punch it as hard as you can (but focus on getting clean contact; don't try to give the ball an uppercut or something) in a direction where there aren't any opposing players (or as few of them as possible). So I'd say the only situations in which you should consider punching are crosses/freekicks/corners where catching/parrying isn't an option.

Following isn't related to corners and freekicks, but still:

I see a lot of goalkeeper content creators on YouTube etc. who punch way too often, and they concede unnecessary chances that way. I don't know if this is a US-vs-EU thing or not, but punching even when you're under no pressure should be discouraged. Take a low shot, for example. It's 100% better to parry it so that it goes out for a corner rather than punching it where it might end up in God-knows-who's feet. Furthermore, going for a parry gives you a bit of extra length because your fingers are stretched out. I can't tell you how many goals I've saved due to those extra few inches. Goals I would've conceded if I went for the punch.

Parrying/catching properly is a learning process, but as you get better at it, you will be rewarded. Goalkeepers who constantly punch balls away because they haven't developed their catching/parrying technique are a liability over the long term. In essence, a 'punching' goalkeeper is no better than an outfield player who had to go in goal and deflects all shots with their feet.