Thank you for this very extensive feedback, really good ideas. I will keep this handy when we will start working on our next redesign on the strategy page :)
Nice to hear that! I didn't know if it could be useful, as I said I'm a newbie Game Designer since there are a lot of things I don't know at all, I will try to figure out more points to improve into the game to give you more feedback! But that's all for today, it was a long night xD
I line the pick idea, but it could be in the same structure as you made the "search champion", where you have a list of all roles, put in what order they shall pick what, and next to it have a list of "all", aka what order it should be picked in. It would then be the same way it is now(with pick/ban mindgames) but be alot easier for new players to udnerstand, and also much much more easily navigated
I already suggested a way to do that with the same interface:
"consider implementing an exchanging champion system in the lobby with random pick orders instead of role pick orders if this suggestion is rejected."
But I'm gonna extend it a lil' more.
Basically you set up what champs get the first pick to the fifth pick, downside the champion image you could set for what lane it is going, so if your first pick is the support and he picks Rocket Girl the system knows that Rocket Girl is for the adc. For having this working it has to be programmed to detect what champions are already picked and where are assigned so if Rocket Girl with ADC tag is picked, the system ignores all the adc picks you have set on the Strategy page.

By the way, thanks to that comment I'm thinking that the system I wrote in the document reinforces the pick/ban mindgames because it adds role pick positioning, so maybe you want your top first picking but there is a chance your rival pick an adc because his player is too good, you might ban 2 adcs and going picking the other in the first pick. That's an example, it's like every match you play is a little puzzle, but of course, there will be a meta around that if implemented but with a few more options.

About making the Pick Order like the Ban Order(I dunno if this is your point), you have to much info in the screen, I could think in a Ban Order interface like that because there are only 3 or 4 bans to choose, scrolling up and down the page the whole time probably make some newcomers lost. It should be easier than it is right now, of course. But we have to think that curious people will enter the game and give it a try, and there is where you catch them, so if they get lost anytime because any reason(e.g.: Doesn't knowing how to set up the strategy pick orders to be as good as the people who knows the meta), they will go out and maybe never come back.

So as a final thought about the general interface, not only the Strategy page, I think that the interface should be as simpler and clearest as the game allows it. What has to be detailed is the simulation behind every match so the game will be enriched with new ones strategies the whole time.

Thanks for your reply!
First thoughts, I don't fully understand what you are trying to explain here but I have a grasp, I will list my feedback.

Champion filters are great
Role pick order is great, if done properly it could allow a flex pick option.
Individual champion builds could be placed into consideration, so, for example, you can pick a champion in a position and assign it's built. This could allow flex picking much easier between different damage types. This would, however, create an extra layer of complexity and increase the amount of management a strategy would take.
The current system for priority picks could be used in conjunction with the role picks, so you can assign each player a champion pool and then prioritizes the champions (without selecting a position) so flex picking can be used as well as aiming for power picks.

I will review it a little more, I do think that the system is confusing but not overly complex at the moment, but it could be more intuitive.

Edit: After a quick review of builds. I realized you can combine both damage types on the build screen and on the champion select screen you can decide between AP and AD damage under each champion, meaning you wouldn't have do adjust builds for individual champions.
I've being thinking on how to implement those ideas, you contrasted them really well so I came up an idea:

It could be another page for that called "Builds" so there you create the builds that you want, then go to the Pick Order page and downside the champion image could be an arrow pointing down, so if you click it, it's shows you a list with the builds you have prefabricated and choose it.
This means the build system dissappears in the Strategy page to be aside in another page, it would be like LoL when they updated the game adding custom builds for champs but centering the system in the builds instead of champs.

P.S: Sorry for being a little confussing with the document, I realized that I have misspellings and even words errors there, this first I wanted to shared it so fast that I didn't give it a look back to the ortography xD
P.S 2 (IMPORTANT): I messed up the ban order desing as it should be the opposite colors for the ban picks, whoops D:
I originally cosidered individual build pages for each champion but I realised that would not be the correct solution on 2 parts. Reason 1 would be it would create a huge layer of complexity where players would need to fix each build before starting a strategy, something you wanted to avoid. The second reason is to do quick changes to builds in strategy, you would need to go to every page and change them individually.

My proposed system, the build remains in the same place but ad and ap are combined and then each champion on the pick order page has a drop down box with damage type of AD / AP.

The advantages to this would be you can mix damage types in the same position, it doesn't require extra complexity in strategy or a long time to setup. The downside is it won't allow mixed damage.
@Ed could you not fix the issue with your idea, being that it wont allow mixed a damage, by instead of having a drop down box, having a slider.
Fully to the left = AD
Fully to the right = AP
Putting it in the middle somewhere would split the damage, depending on how close to each side you put it.
Oh that would work as well, as long as it's under each champion. Maybe keep it to fixed increments like 0 to 10 so players aren't spending too much time micro adjusting. Nice idea.
Yea, nice one, I suppose I wasn't thinking to much in how it affects the players, but I thought it could be kind a problem when it comes to customization.
You are able to set if you are AP/AD/Mixed, but you can't set AP OffTank/AP Assassin... So maybe could be two sliders instead of one, something like this:
So if you set the slider on DMG the player would focus on buy damage items and in DEF he would buy deffensive items. It adds another layer of complexity to set the strategy as you have more options available, but it's not going to mindblow the players and also that should lead to another types of strategy.
What do you think?
I feel this could be a great initial change. Maybe just damage to start with and then consider tank stats. That would need another update in my opinion to champions.