If I were the instructor, I think I'd be more scared than the students.
This is my perspective as an instructor.
First of all, I've done many hundreds of "intro" dives. All of which have been in the pool.
I'll tell you how I approach it and why I think it's safe enough when you do it like that.
First of all, it starts with the material and information. Students watch a video, answer some questions, get good instructions on clearing ears and not holding breath etc. and we play with the gear (especially the inflator) for the fist time "dry".
The briefing is kept easy going and the message is made very clear that this dive is intended to be easy and fun. I don't lay a bunch of "information overload" on them but instead talk more about what prompted them to want to try it and to try keeping the intro conversational.
All this leads to them arriving at the pool eager (in most cases) to get in the water and feeling relaxed about it. This is SO important.
In the water I start out in a shallow part of the pool (waist deep) and do two exercises with them, reg out/in/clear and mask partially flooded. I don't teach it necessarily to the level I would in OW and it's not intended as such. It's intended to show me who the "concern" cases might be. The shop's "lead" instructor used to give me flak for doing this because in his mind it make things too much like a "course" but I didn't listen to him. I need to know who is going to be a problem and who isn't. Period.
Then we make a little bimble around the shallow part under water and when everyone is feeling ready we swim into the "big" part of the pool one at at time while being held as they descend and clear their ears. Once everyone is in the deep part (2 meters) we go as a group for a swim around and then do some stuff.
I usually take a frisbee with me, which is a big hit, and the divers are basically left to do whatever they want. I tell them to try to do some of the things I'll be doing (which includes somersaults, barrel-rolls, hovering, swimming backwards etc) and that if anything unexpected happens that they just swim to the surface, inflate the BCD and wait. In fact is was during intro dives that the coin fell for me and I realised that it's not difficult at all to teach hovering and/or doing skills neutrally buoyant from the onset.... but that's another thread.
The pool isn't small so if I'm working alone with a small group I'll work out of a corner so I can keep them corralled where I can see everyone and intervene quickly if needed. If the group is bigger and we're working with many staff then we'll surround them like orcas keeping a ball of sardines together and whoever is closest when something needs attention takes care of it.
The hitch is this. If in the shallow end, I see that someone is going to be a "problem" case then I'll send them 1:1 with a DM while the rest of the group goes with me. In some cases they don't get into the deep end at all. In one case I can remember, the diver didn't get under the water at all.
Problems are all dealt with on the surface, and things like "can't clear", "cramp" or anything else that might cause discomfort and goes against the "easy" and "fun" mantra I told them about means we just wrap up early. Some people even decide after 5 minutes that it's not their thing. That's cool by me.
Some people also have to be dragged out of the pool after an hour and those are the ones I'll talk to about taking the OW course. Everyone who comes is given (this was shop policy) a shop business card that could be exchanged for a free intro dive. The student could use it themselves, hold onto it to cash in for an extra session during the OW course, or give it away to friends. This is also to ensure that the ones who stopped early and think later on that they should have stuck it out can also try again if they want.
Done like this the bar is kept low, it's fun, it's easy and the risks of major problems are dealt with by (a) making sure people who "concern" you from the onset get 1:1 supervision, (b) keeping the group closely supervised and confined in relatively shallow water and (c) not forcing it when it becomes uncomfortable.
Obviously this is a particular context but in this context I think it's safe. I know some intro dives are done in open water in 5 or 10m depths. This would make me uncomfortable for a first time experience.
R..