You won’t be running a Pi5 without a cooler, the kit costs 79$ or 99$ (for the 8GB of RAM). I never said it was over 100$.
Now HP Mini i5 8th gen + 16GB of ram + 256GB NVME that obviously has a case, a LOT of I/O, PCIe (m2) comes with a power adapter and outperforms a RPi5 in all possible ways costs you 100$ as well. And then there’s the 4 and 5th gen Mini PCs selling for 50-70$. If you want even cheaper then look for i3 CPU + 4 GB of RAM, you’ll find 40$ complete machines that run faster and are way better than a Pi