At that point why not just create one official competition map and always play on that? That's a serious question by the way. Why not just have an official map for such contests so that everyone has an even playing field?
This is in fact the entire concept of the BOTM (BtS/game of the month) contest. A mapmaker makes or rolls a map, and everybody play that, so it's a totally even start there. Though things can quickly go differently ofc, especially if random events are on. But I like that setup much better than HoF, because you can just jump in and play a map, and everything is more or less comparable afterwards.
I didn't really mean to badmouth HoF here, but it is a very specific way of playing, and it's certainly not for everybody. Yeah, there are still many slots that can probably be beaten with a more normal map and without lottery numbers luck, but that also means that somebody else can easily beat
your score/date if they really try.
For these games there are some rules that the required mod checks, like min/max amount of AIs. On Huge maps you can choose 18 civs, which is the most possible without mods. On some map types, the land will then be pretty filled up, and there won't be long stretches to the nearest AIs. Some map types are larger than others. You can pick and choose depending on what you want to achieve, then roll 1000 to 10 000 maps (with a program called MapFinder), and pick what looks most promising. So first you stack luck on top of each other, then play a bunch of super start maps, and continue the one where you have godly luck with RNG or non-hill cities or whatever. Another person that go for the same "slot" and just roll a random map with random civs and "let's go" will naturally then stand zero chance to compete. It's the nature of the HoF beast. For better or worse.
BOTM is more interesting (to me) for a few reasons. 1) it's a level playing field, and 2) the maps or scenarios can be very unique, in ways that is impossible with a randomly rolled map. Those are probably the two main reasons. Plus it feels a bit more friendly in nature than some of the other types of contests on this site.
About the team maps, then yes, several people play on the same save. Let's say you play 20 turns, then hand over the save to me, and I play 20 turns. Then somebody else plays 20 turns, before perhaps you play 20 again. Or any number of turns really. It's more for fun and cooperation than anything else. Even winning is secondary. Then you have discussions in between sets, or during them, about what we as a team will try to do. Kinda similar to the SGOTM, except
much less competitive, with less strive for perfection.