The start of AotC does a really good job at actually introducing each character with the exception of Qui-Gon and Shmi, though when you think about it, who the hell is Jedi Master Syfodias? I guess because he exists without an explanation in AotC, Qui-Gon and Shmi can be largely omitted too. From the opening scenes in the movie, you knew who Padme was, Chancellor Palpatine, the key Jedi masters, Obi-Wan and Anakin and their relationship to Padme as well as the overall unrest that's going on in the galaxy.
I was a little sceptical too, which is why I spent the other day watching the movies all in a row in this order to see if it would actually work... for whatever bad acting and awkward moments AotC has as a movie, it seems to handle simple character introductions and short expositions very well, exceptionally well compared to TPM... though maybe still not as well as ANH did it. The movie told you pretty much everything you needed to know right at the start.
RotS on the other hand assumes you know exactly what's going on because it makes absolutely NO attempt to explain anything, it's just running right when it hits the ground and it's off. The only thing that's explained is General Grievous' role since he's a new character to the movie.
I think the reason why AotC works well as a starting point for the prequel era is because of the 10 year gap between TPM and AotC that requires that people be reintroduced again and the setting be re-established. And the thing about TPM is that after this 10 year time period, the specifics of TPM become largely irrelevant. Actually, the interesting thing about AotC without TPM in this lineup is that the reveal of Sidious at the end of AotC is a huge "holy ****!" moment cause you just saw that guy talking to Darth Vader in the middle of ESB and he's still this really mysterious figure you know absolutely nothing about but you know he's this pure evil lurking in the background... and being more of a phantom menace than he is in TPM itself o.o
And you're right about the only stand alone movies being TPM and ANH, but in my view, AotC and RotS being preceded by ANH and ESB takes the place of TPM in explaining who these people are and why they matter because all of these characters and events are talked about in those two movies already.
So no, I wouldn't get people to watch only ESB and RotJ or only AotC and RotS, instead I feel that ANH and ESB make a better substitute to give people all the information they need to know who the people are in AotC and RotS and the events that are transpiring since the events that happen are so closely linked, the Clone Wars and Anakin's fall to the dark side being the most important key points.
So because TPM and ANH are capable of being stand alone, that means that if people want more Star Wars, they can always watch TPM if they're interested... it'd be no different than seeing a prequel (lol) movie of a series that just happened to have a flashback part in the middle of it. Plus there's no reason why people shouldn't also enjoy some Clone Wars as well while they're at it and if they're interested.
Overall, when I did watch the IV, V, II, III, VI order, it made quite a lot of sense and made it a more manageable viewing experience. It also made RotJ SO DAMN AWESOME. I mean, seriously, that downer you get from the end of RotS just makes the high at the end of RotJ just that much higher.