Expanding on the above a bit.
Microphones come in a range of operating principles and designs. There is no such thing as a perfect microphone, and the various requirements will dictate the best choice.
For live use a lot of requirements are relaxed, but new ones added. First up is robustness. Live is a punishing time for equipment. Yet failures are intolerable. Many studio microphones would simply not survive. A ribbon for instance would not even survive being set up on stage, let alone actually being used. Robustness favours a dynamic mic, but many condensor mics are pretty robust. Phantom power is ubiquitous, so powering a mic isn’t an issue, but you would not be wanting to set up a power supply for some prized tube mic.
Proximity effect is key to a vocalist that understands how to use it. Also a skilled vocalist knows how to use the varying off axis frequency response as well. This allows the vocalist to tailor the sound of their voice as a means of dynamic expression. These effects are the province of large diameter microphones, as they depend upon selective cancellation of frequencies with distance across the microphone membrane. So, this also favours large microphones, and is why the old RCA style mic has never gone out of favour (although it is a ribbon, so not really useful live). Vocalists that know their craft will usually have a favourite microphone, one that suits their voice and style.
A small diameter condensor microphone, as seen by some modern vocalists, especially those that are more song and dance merchants than skilled singers, pretty much dictates a fixed response, and suits a vocalist whose only job is to basically sing the words. Given many such performers will have their voice harmonised before it reaches the front of house mix, it really doesn’t matter much anyway.
Small diameter microphones have higher intrinsic noise than large microphones, simply because the larger ones average more noise of air molecules hitting them, and this can matter in critical recording applications, but live matters not at all.
There is however no doubt that the microphone as stage prop is also pretty important. It announces visually who is in charge, and gives the timid something to hide behind. It is clear some vocalists feel naked without something to do with their hands whilst the rest of the band are more obviously occupied.