To answer your question, yes you can. You can do anything you want with plumbing but at what point does it become a nightmare or against codes designed to protect you and your home from danger and damage.

It is very simple if you just want cold or just want hot water coming from it. If you want to have the ability to do both, then it becomes more complex and expensive and, prone to inevitable leaks.

For example, if you just want hot water, you can T off the hot water line. You are totally dependent upon the water being turned on or shut off at the spray head. You already know they aren't reliable. So then you'd have to install a shut off valve. Now it becomes complex and cumbersome. The all in one faucets have the manifold,mixing valve and shut off to the spray head all built into one.

yes, it can be done. With a separate handle for the spray, you get mixed water (hot and cold, mixed according to a single handle's position). This makes it a 2-faucet kitchen. It costs less to have a separate handle, on a "mixing valve". You could build a linear protrusion ("wall shelf") to hold a wall mount faucet and a wall mount spray. Each one controlled by a handle on a mixing valve.

What did you end up doing? I'm in the same predicament.