Speed for one, I don’t know how large your HA install is, but the more entities you’ll get the slower your pi will become in running HA. I have over 1200 entities and I really prefer it to be running fast.
There is another reason why I would not recommend a pi, simply because it isn’t really flexible in terms of upscaling. (What if you want to run Plex and a ton of other plugins?).
I run Unraid on an i5 4690 with 32GB of RAM and have around 40 containers running. Processor usage is around 11% so it leaves me plenty for additional VM’s but will also allow me to transcode 1080p streams without hiccups. (4K is different unfortunately and will still require an even more beefy processor or a GPU that can do transcoding for you).
In most cases, most people will not need this. But having a system ready for expansion is never a bad idea imho. Plus you can have the ssd internally instead of a USB external one (which could save you from accidental stuff like pulling the cable). And then ofc performance, my HA restarts in under 5 seconds with all the components and such running within 15 seconds. I am betting that you won’t get this kind of performance with an rpi.
Honestly, people should do whatever they are fine with, in my view though a rpi is a hobby product whereas a NUC is more of a permanent (more professional) solution. If you have not tried other hardware than a pi to run HA then don’t, if you don’t know what you are missing it is best to not know until you do have the hardware. Why? Because it is hard to go back.
See it as follows: HA is the heart and brains of your Home Automation (like an engine would for a ferrari). Now imagine having a ferrari, but only running a 1.1 toyota engine or a Ryzen 3950x with a GTX 1050). To me the heart and brains are the most important piece of the setup (as without it, it simply doesnt work). I see people on this forum spending thousands of euros on smart stuff yet they use the cheapest form of system available.
Why people would choose a NUC is because of the low power usage (like a rpi does) but with the performance close to a laptop. Building your own server is another option if you dont care about power usage that much (which is what I did).