The question really comes down to "how small is too small?"
Some people think a 125cc limit is reasonable because it keeps inexperienced riders off of interstates/freeways where things move too fast and a small accident is likely to result in a major catastrophe. Personally, I think freeways are the safest place for anyone to be most of the time so I don't agree that newbs should be kept off freeways.
Some people think you need to be able to go 0-60 in 4 seconds to merge onto a freeway safely... I've never found that to be the case. I'm a fast/aggressive merger and 8 seconds is usually plenty.
I think that beginner bikes should be capable all around... they should allow the rider to explore different types of riding... aggressive canyon riding, touring, commuting, cruising, ideally even dirt roads and the like... until you've tried it you really don't know which type will be the most fun.
They should also be well mannered... keep the traps for the unwary in the engine, suspension, and the like to a minimum. Not because they can't handle those traps, but because they may not be able to handle a killer throttle and a weird road surface and a cell-obsessed cager all at once.
They should also be practical. That means you can use it to run errands, to get to work, to go to the park on a weekend, to cruise around on... because too many "bikers" only ever ride to bike nights and bars, and they never develop much real-world riding experience. Doing something every day allows you to learn *much* faster than doing it even once a week.
Finally they should be cheap... because frankly a lot of people ride less that 1000 miles total in their lives.... you see it around here... a few months ago someone was posting about how they bought a brand new gs500f and had taught themselves to ride in only a couple hours with no training...and a few weeks ago that same bike appeared in the for sale section w/ 700 miles on it. "Helmet included if you want it."
I've pretty much given up on trying to explain the safety difference... yes, some bikes are more dangerous... but you aren't going to reach all that many people by telling them that a <whatever> is too dangerous for them. You may reach them by telling them it costs too much to insure... people are more constrained by their pocketbook than their bone denisty.. but that doesn't always work. I was sitting in a fast food place the other day listening to two of the employees talking... apparently one of them had just bought a car, and they were discussing insurance... "only $400 per month!" I almost soiled myself... but they were really pleased that with their tickets and accidents or whatever it was only five thousand a year to insure a car.
There is another issue that I think is probably even more important... but much harder to express to people or convince them new riders how important it is...or even how to select a bike based that is "good" in this way. That's the idea that the bike you start with will establish habits and patterns for you that will be extremely difficult to break later on, so you want a bike that encourages good habits. If you have a bike that accelerates better than it turns or stops, you are a lot more likely to view the throttle as your "accident avoidance control"... and that's extremely dangerous. If when you really hit the front brake the nose dives and at that point will skid the rear wheel if you even brush against the rear brake pedal, it will change how you hit the brakes on panic stops... and perhaps not in a good way. The much-recommended ninja250 does that... I can't tell you how often I've locked the rear wheel just by increasing pressure on the front brakes without adding more rear brake at all. The rear brake is mostly good for trail braking on curves, not for helping stop the bike more quickly.
Confidence, especially in real-time dynamic activities like riding and flying, is an absolute essential. There are times when the only way out of a situation is to do something risky, and do it NOW ... in riding it might be pushing a little deeper into the curve... in flying it might be pointing the nose further toward the ground... in any case you must have the confidence and control to do it even though though it takes guts. A newb bike should give that confidence... even though there is a chance that it will cause brash risk-taking. Brash risk taking is probably less risky than someone not thinking they can make a curve they are committed to making and causing a panic-induced highside.
More than arbitrary HP limits that riders will ignore with a blithe, "I'm an above-average driver, I can handle above average power," we should try to steer people towards bikes that will make them good, safe, and confident riders as quickly as possible.... and show them the broadest range of riding types possible... so that they can have fun, be safe, learn well, and actually benefit from riding for years to come.
I just have no clue what bikes would do that... so I'll probably keep recommending the ninja250.
Ride it like you think owning it matters.