The rim is the limiting factor.
Yes, they could probably make modifications/redesign their magazines to accept 15-20 rounds in a straight mag but, to them it just isn't worth the cost/effort.
What is possible however, is a single stack magazine in the shape of a "U" to allow twice the current capacity (giving you approximately 20 rounds). It would be similar to the teardrop mag for the Ruger 10/22 as to how it works but, it would look much more like a ordinary magazine.
A MS paint draw up for those of you who don't know what magazine I'm talking about:
The red one is the follower.
Now look at your kids airsoft pistol (namely the Sig P230 clear), it's has the basic idea.
I believe the reason that the teardrop mag is a teardrop and not perfectly vertical on both sides is to improve the reliability. You don't want the bend (bottom of "U") to be too tight because you don't want the ammo to bind in the bend and you would want a strong spring and well designed follower... The follower should be like a rolling pin and connected to the spring, not just sitting on top of it. Now that you have the follower round and rolling, you will have issues of mis-feeding when you come to the last round - in order to get past this, you will need to make a section of the follower have a groove recessed into it (the rearmost portion of the follower)... this recessed portion will need to be able to follow the .22 shells lead and rotate accordingly, not freely like the rest of the follower.
It can be done and you would have your standard capacity magazine. This obviously would not work for current pistols so, a manufacturer would have to design a new pistol around this magazine.
...Everybody loves new .22's - Just look at the Rhineland R22 - which makes this a perfectly acceptable option for a manufacturer to take hold of. I would just ask that they not make another Beretta Neos or other odd looking pistol. Keep it simple, and maybe even traditional.
Look at Ruger and their factory magazine... Basically a revolver, evolved into an auto. It was innovative and thought up by creative minds. Reliable as hell too.
If only Bill wasn't a wuss, we might have even seen this design come from him.