it can't be due to "technical limitations".
It actually is due to that. Vooks did a great article on the subject, pointing out how Nintendo typically likes their Virtual Console games to be uniform and have similar features with one another, from restore points, suspend points or fancy borders, among other things depending on the system. The Ambassador games have none of those. Heck, they don't even go into sleep mode or allow you to multitask during the games, and compared to playing on a DS Lite (From personal experience), the colors are worse and the games don't feel engaging to play. Growing up with Kirby and the Amazing Mirror, Yoshi's Island and Minish cap, I was only able to tolerate completing Kirby 100% since I love that game a lot regardless of the circumstances, but the other two weren't really fun to play on the 3DS for me so I'd just pull them out and play on my old DS Lite if I wanted to play them on the go.
That being said, FE Sacred Stones ended up being my favorite of the GBA games solely because of how surprisingly good it was compared to Shadow Dragon (The only FE I played before then, which I HATED), and how quick and easy it was to suspend the game at anytime, making the issues from the GBA VC irrelevant.
Still, I can understand why the GBA titles aren't on the 3DS VC. If they can't have the fancy features NCL wants them to have, then they don't consider them "quality" ports and won't be released. Heck, SNES games came to the 3DS VC on N3DS only because of the extra things like the screen resolution and restore points, so it's really just a matter of them being picky. I prefer to play GBA games on my Wii U anyway because of how crisp they look and because I can use a wide variety of controllers (like the excellent Pro Controller). DS games on the other hand, I feel are pushing things a bit too far, since you can only use the gamepad and can't remap buttons for some dumb reason...
As for why SPM doesn't support the gamepad or Pro controller, its mainly due to NCL not classifying the Wii line as Virtual Console games, instead going for a more technical term of "Wii Retail Downloads" due to them being pretty much the same as putting a wii disc in. Doesn't stop NOA/NOE from making typos on the matter, however. :p