What is the purpose of qualifying series?

This is likely going to be quite the long post, for that I apologise. I want to emphasize that this isn't a "QQ-thread" or similar, although I will admit my recent frustration due to a ranked loss did motivate me to write this. I also apologise for any language errors, I'm not from an English speaking country, although to be fair that rarely seems to help.

So, to repeat the topic: What is the purpose of qualifying series? That is, why do you have to win a best out of three, or best out of five in order to increase your rank (after already having won your latest game in order to get to the series, I might add)?

Let's investigate what would happen if there were no series, that is to say, you would simply move up a rank if you reached 100 LP. As far as I know, matchmaking, however dubious its actual mechanics, tries to converge your MMR so that you have approximately a 50% chance to win. This means that even if we removed the series, you'd still wind up stuck at your skill level cap (or "skillcap-rank, as I will be calling it), being unable to achieve more LP. The big difference, and what I think is the main advantage, is that you would get to your actual skill's rank much quicker than the current system, with - in my view - no actual downside.

Now on to what I consider bad/annoying with the current series system. As we all know, you sometimes get a team that is, to put it humbly, not playing as well as you'd hope. Sometimes, perhaps as often as aforementioned team, you get a fantastic, stellar team that exceeds your expectations. Most of the time though, your team and the enemy team should be fairly equal in skill. This is where your personal skill comes in, and where you can shift the tides in your favour, so to speak (and this is also my main argument why there is no "ELO-hell", but that's a completely different topic). This will mean that you win most of the games with equal teams (if you are below your skillcap-rank), win the games with fantastic teams, and lose (at least most of) the games with less than equal teams (where it's to your disadvantage, I mean). Now what happens is that you advance and over time gain more and more LP, if you are currently below your skillcap-rank, and eventually hit a series. A few combinations can happen in these best out of three (or five) games with regards to your team and the enemy team. If you're very lucky, you will have two games with a fantastic team whilst the enemy has a less than avarage team. If you are very unlucky, the opposite. This all seems fair. Eventually, if you play enough, you'll get an equal amount of series where you are lucky, unlucky and in between. However, it is also possible for you to get stuck, and have to play anything from two through ten or more (if really unlucky) series before you get enough good luck to move to the next rank. This can happen even if you're way below your actual skillcap-rank, since it's very hard if not impossible to carry completely alone (again, only if you have very bad luck with your team and the enemies are all very good). Now, of course this isn't a real problem if you have tons of time to play, you can just play a few more matches, you'll be in another series, maybe that one doesn't succeed, no matter, you have time for more games. For me personally however (and I for many others I presume), that isn't the case. I'm a law school student at university, it's my final semester and I'm writing my thesis; thus my free time is quite limited, making it possible for me to play only about one or two games a day on avarage. This means that if I have bad luck, it takes a long time to climb, even if I'm far under my skillcap-rank (which I'm sure some of you will argue that I'm not, and that's fine, personally I think I am under it, but please, try not to focus on that).

I would suggest then to remove the series completely, making it possible to continue to climb so long as you're winning more than 50% of your games. Why do you have to win three out of four games (if you recall: you have to win the game getting you into series, and then two more out of three) to move up? Of course, if series were removed people might be fluctuating in between two ranks/divisions much quicker (if for instance their skillcap-rank is just between say Plat 2 and Plat 1 they might fluctuate between 70 LP Plat 4 to 30 LP Plat 5), but where's the harm in that? Would it not motivate you more if you increased your rank quicker if you started playing better and vice versa, could drop quicker if you played worse? Also the fear of dropping wouldn't be as considerable since there's no time consuming series where you might have bad luck and get stuck that you have to worry about.

Please discuss, and enlighten me about the purpose of qualifying series. Rioters are welcome to join in on the explaining, of course. Thank you summoners, McCrackon out.

TL;DR Why have qualifying series, why not just rank up when you reach 100 LP? Series forces you to have to win 3/4 games, and if you have bad luck with teams, it can cause you to get stuck, which is annoying if you don't have a lot of time to play.