I'm not sure why Flygon has never been owned by anyone in the main cast thus far considering that it's one of the most popular Gen III Pokemon from the look of things. Then again, Lucario's popular as well, yet it was never owned by a cast member either. I don't know what factors the writers use when they decide on which Pokemon the cast members capture these days, in all honesty.
People thought Rica Matsumoto choosed some of Ash's pokemon in the show, but she debunked the theory herself.
IDK, in terms of marketing, Kanto/Johto (which were basically pikachu + starters, with some randoms mixed), Unova (starters + event scraggy) and shamelessly Alola had it in spades with Ash's teams. I take the other teams just had more freedom to be built. Yeah, things as flygon, braviary or lucario would sure be material for a protagonist's team if we're going just by their design. In flygon's case, I think it just wasn't promoted enough.
Lucario it's more singular, since the thing is shilled the hell out since its movie and have basically appeared every saga since Sinnoh as some sort of variable boss level opponent. I mean, it already peaked its popularity, it's already a timeless pokemon that can pretty much fit into any protagonist's team with no much problem, independent of the current generation and without steal anyone's spotlight, if we take Kiawe' charizard as an example. Or that boy from movie 20 who had a lucario that was basically a walking action figure. The only reason I think Ash hadn't one in Sinnoh was because of infernape (who ironically stole everyone's thunder). Nowadays, who knows?
Doing this again for 8th generation (This only deals with the new Pokemon; including Galarian Forms) I'll make another list for the old generation Pokemon I would like Ash to catch)
It will be in Spoiler tags, so only look if you want it'll also be pretty lengthy, because I went over every Pokemon why or why not Ash should get said Pokemon. This is entirely my opinion. I want to wait a quite a few episodes before deciding on anything more solid.
Dunno, if I go for hattena's line dex entries, have someone always hype and noisy as Ash training a pokemon that prefers calm and collected persons looks endearing. I'd like, but I don't think the anime staff would give him one, anyway.
How? Ash has worked with meek Pokemon like Sobble before
Probably because intelleon it's slightly androgynous. Not enough of a reason for Ash don't have one, though.