If you are only streaming music then a Pi4 is overkill and a 3 or even a 3a will do fine and run much cooler. I've built players with all 3 types. (squeezebox and LMS)
Not really. It depends on the DAC you use. If you use an I2S DAC, then yes, RPi4 is overkill
If, on the other hand, you want to use a (usually better) USB DAC, then there are quite a few well documented cases where the RPi3 USB implementation (shared with networking) can cause audible glitches. Given that the cost differential of a RPi4 over an RPi3 is negligible, especially once you add everything else you need to make it work, including your time to setup things, using an RPi3 is a bad tradeoff, IMHO. A lightly loaded RPi4 doesn't need cooling
A 1Gb RPi4 costs exactly the same as a 1Gb RPi3, and 1Gb is more than enough. Why would anyone buy an RPi3? You need a case anyway, and a cooling case costs just a little more over a non-cooling case. And you have better future proofing