I own a musical saw. I have found it very difficult to get started, and gave up before being able to play a simple tune with any kind of fluency.
The first challenge is to coax a clean note out of the saw. You must bend the saw into an 'S' shape, and bow at the resonant position. If you bow in the wrong place, you'll get an ugly scrape. If you bow in just the right place, you'll get the pure ringing saw sound you're used to. There is a right amount of pressure - too light and the sound will be thin. Too heavy and the sound will be dull.
Many people use a "cheat" to make forming the 'S' shape easier - this is a wooden handle with a slot into which the end of the saw fits. It just gives you some leverage instead of having to hold the end in a tiring, vice-like grip.
Then, when you change the depth of the 'S' to change the pitch, the resonant position changes, so you have to bow in a different place. To play fluently, you need to constantly move the bowing position to correspond to the pitch.
On top of that, as you've already noted, you have to intonate by ear - which may or may not be a challenge for you.
Perhaps with one-to-one instruction it would be easier. I think with a teacher telling me how much pressure to apply to the bow, how much rosin to put on, and so forth, I might have got further.
I still believe it would be an extremely satisfying skill to gain.