First of all, Lulu is very similar to Janna for the intended role of peel support. Yes she has some very different aspects but at the end if you know Janna quite well, you can pick Lulu without a problem. As i said atm the only "mastered" range supports that have good peel are Karma, Zyra and Janna(dont count thresh in there). Since Karma and Zyra are quite niche, if Janna is unavailable, picking Lulu support even with less experience is a better choise most of the times. Even Nami with not so great bubles. For example, Ezreal pairs quite well with Lulu as she can peel, help with wave clear if enemies are going for it, and add to his poke. Karma cant do that, even if on paper it seems like that. So if i need a peel support, why should i be punished in that case?
Second, your idea is a handicap to veterans that did not have time to grind masteries. Due to external reasons i did not have so much time to play at least last season. So my skill atm is rusted but still i did decent on my few ranked games. If i pushed more, i could climb maybe to plat. But since i did not i was gold 4. That was fair indication of my skill at that moment since i was not keeping up. I should be expected to perform on that level no matter what character i play. But on the contrary i had very good games on unmastered Swain and Zerath as they were for a long time my goto safe picks for top and mid, my worse lanes. Also a decent unmastered olaf jungle. That i did 4 bot games to optimize jungling speed.
Addition to second point. Someone mastered a champion when masteries went out and did not play with him since then. How is that different from eg me not having a mastered Lulu that was my favorite support for a long time? Or the real example of Swain. He(along with J4) is the only champion i can feel safe top lane and was not mastered when i was forced to go top. Countered Olaf and all good at top lane.
Last and most important you did not touch at all the swap reason. For example our first pick is a great anivia player. But he is afraid of counterpick. I have her but since she is not mastered, i cant pick for him. This is a great handicap. And i cant grind so many champions just to swap. Even if it is only for powerpicks, i am gonna play many games without having any fun at all, with all the frustration both to me and my allies.