I use a 1hp 14" Jet bandsaw for sawing up logs to make boards.
I can saw a little over 12" thick. most of the time I'm sawing 4ft long logs.
Hickory, Oak, Maple, Ironwood, Cherry and some other odds and ends, all hardwoods.
I use a Bimetal blade with 3-4 pitch, 3/4" wide.
Biggest issue I have is the blades will break before they don't cut.
The blades will start cracking from the gullets and eventually will break thru. I can usually tell when sawing when they are going.
I have stalled the motor a few times its not an issue really.
I can make a cut thru 10" thick Hickory 4ft long in about 2-3 minutes.
I typically will saw something like a 12"dia x 4ft log into 1 1/8 thick boards and will end up with 7-8 boards. I can saw something like 8-10 of these logs before the blades will usually break.
I think I could really improve my production f I would of gone to a bigger saw, something with 18" wheels that could run a 1"-1 1/4" blade.
Also really helps to saw relatively dry logs, Green logs tend to deposit sap on the blade requiring frequent cleaning of the blade.
So as to OP, yea smaller stuff is limited.
Trouble is you have to get machines in the sweet spot of what your using them for. A big machine is nice but it takes more room, bigger blades, more power. Going too big will certainly do the work but it has other draw backs.
I think in most newer lighter built machines its better to go a little bit on the too big side rather than just right size.