How to measure speed, (without using a Hall Effect Sensor)?

I'd think so. There might be specific applications where this is not well suited, or another solution is better. You can get pre-made disks for these photointerruptors that fit onto a standard consumer DC motor:

Having everything out in the open could be an issue in a dirty environment. If the LED or phototransistor get covered with dust and grime, they're not going to work. It could be a good deal of work to make an enclosure.

You can get one-piece rotary encoder modules that are all enclosed.

You can get encoder motors that have everything in one package, though a lot of them are Hall effect.