I want to preface this post by saying you seem to be asking a question that has answer that doesn't help your problem, but I could have just completely overthought the problem. Your problem seems to be you feel the probability that a player knows the role they call is more likely than them not knowing it (hence, why would they call it?), that you don't want to take it and risk losing the lane, ending in a loss that could have been prevented if you just gave the champion the role they wanted. If you find your preferred role, but you still give it up because you'd rather not be at fault for losing the lane, then what was solved? In general, I do fill/give players the role they called as preferred, but when I've lost more than one or two games because of people calling a specific lane, getting it, and then losing it, I just determine what I feel like playing (roll dice if you absolutely can't possibly think of a preference), say "i would highly prefer to " and then just obey pick order. You will get the role you're looking for lots of times and maybe do some filling. Personally, I'd prefer to lose a lane myself than relying on someone else, unless I personally know them as a good laner (my IRL friends I play with).
If you just want help selecting a preferred role, then:
TL;DR:
1.) "I am self-aware, realize my actual skill level in the game, and adapt/learn quickly" (What I fall under)
Me (since you asked): I don't have just one main/my main constantly switches; I know all of the champions well enough that I can look at the list and find out what I think will be fun, spend some time with them in custom/normals, and then ranked until I'm bored with them and select a new champion.
Others: If you adapt/learn quickly but don't have the same problem with boredom, then either:
.:Choose a role/champion you find to be your favorite/you have the most fun on/you feel you win more often
.:Use a website like lolking or lolnexus to determine the champions you've won more with and try to call/win that role as often as you can.
.:Liike I stated before, if you absolutely can't decide which role to play because they all, or four of them, or three of them, feel equally to you, assign roles evenly to numbers on a dice and roll the dice (left over numbers when assigning 4 and 5 roles are "roll again")
2.)"I feel like I am bad at the game/I feel like I don't truly understand the mechanics of the game/I don't really adapt to new kits easily/I tend to just enjoy what I've learned and taking the time to learn new champions is too to me."
I know you said you typically do fairly well in lane and some of those mention being bad, but none of those particularly go together, they just have the same advice: Take some normals and play with champions considered FOTM, hypercarries, or freelo, and choose your favorite. Google basic laning tips if you're told you have abysmal CS or you feel you typically aren't doing as well as others.
Long version:
I think it depends on how self-aware you are and what you realize your actual skill level is. At the moment I can't study your match history, but you said you can play your lanes fairly well and I'm just going to take your word for it. What I mean is, if you don't understand the basic strategies for winning your lanes (when/why to push, how to freeze, how to make minion waves push towards you, last hitting in general, last hitting under tower, and so on), it doesn't matter what you choose to main. You're only going to do well against an enemy who does these things worse than you (in general, I mean. There's always room for exception).
For me, I don't have a main because I don't have enough spare time to invest into League anymore. I personally know that if I jump into normal games for a day or two of play, and focus on really learning and playing two or three champions, looking online at current builds if I can't figure one out from their kit, I can learn everything I need to know about those champions that my wins/losses stay around 50%. But.. because of how often I get to play, I just take a champion (usually one I've spent a lot of time with in the past) with a kit that entertains me, and I play them until I get bored and then switch it up, but my lack of time investment has caused me to lose my edge and drop to bronze 5 for this account. My point is, if you're like me and have an easy time adapting/learn things in life a little more quickly, you might not really have a main in the sense that there's a specific champion or lane/role or class of champions that matches your playstyle while other champion classes hinder you. You'll be able to just choose either what you feel like playing, or who you think will bring a bigger advantage to your team. However, if you don't spend any consistent time with a champion, you can't learn them well enough to be very useful regardless of how quickly you can adapt. Whatever role(s) or champion(s) you pick, make sure you play them over and over, make sure that if you're not doing particularly well to look for builds online and compare the differences.
However, if you don't adapt well to new kits, or you generally/always have some negative feeling concerning learning a champion, or you don't feel like you are skilled enough to utilize the full potential of most champions, then try and determine what your favorite playstyle(s) is/are, play the different champions in those roles that are considered as OP, FOTM, hypercarries, or freelo, and learn them inside and out. Do you like to flex your inner glass cannon and burst down your enemies? Do you like to absorb damage for your team, preventing the enemy from escaping with your utility? Are you more entertained by zipping around making plays with your mobility? Blinding attack speed that intimidates enemies from getting too close?
As always, don't just choose one role/champion to master. Learn two or three and play them as often as you can. They may get banned or chosen by the enemy, and you'll need a contingency.
. But after i tryed 
. And i took him again and again. I liked tanky champs. Today I made my list of playable champs lil bigger. I allready play 
. Think to buy soon 
and maybe to start play 
after update will be released on server. In situations I can't take top, i go as support 
.