I have two saw arbors. The smaller one was home made from a purchased blank MT1 arbor and has no key. It does tend to tighten (as Michael suggests) because of the R/H screw used. I use it on my small EW lathe with a purpose made table to cut small brass sections – which it does well and it doesn't slip as far as I can tell.
My Chinese MT2 1" arbor gets mostly used on the Atlas MF instead of the overhead arbor. It has a key (which I use) and a L/H thread. This is also used mainly for cutting brass sheet (where it's length is a factor) using either the edge of my sub-table for support or on a sacrificial plywood platform if I need a deeper reach or some kind of custom hold-down (e.g. strategically placed screws!)
None of my slitting saws are hollow ground (that I'm aware of) and none of them have any kerf. I'm always very cautious when using them and would think very carefully before trying any very deep (long) cuts with them – something for which they are not designed for in my view – at least the thinner ones. I have several other means of making deeper cuts if required – either with milling cutters with proper side clearance – or using saw blades with a kerf (e.g. in either an Armstrong or a power hacksaw).
Call me chicken – but there you are!
Regards,
IanT