Ok, so starting 7th August 2018 (or whenever update came to people), lots of Windows 10 Insiders had this issue with game, in form that after champion selection game simply won't start, and you're immediately kicked back to "Reconnect" button on empty screen, while game seems to be not aware that you are not there, and you get penalties for AFK.
Problem actually can be related to Windows update 17730 (RS5 RC). With that release, Microsoft changed the low level network TCP layer stack (to what is called Cubic), adding HTTP/2, network speed improvements and whatnot else.However, it seems that some applications ended up acting strange while perusing UDP subset of that layer. One of such apps is LoL, but there are others too (won't advertise, but some versions or famous remote desktop app has same prob, few QT based apps, etc).
Since 17730, there was another Windows Insider update 17741. This update didn't help to solve the "Reconnect" problem, but had made Hextech Tool crash as well (on gathering process list, it just closes).
So, for players, either use install from image of older Windows 10 or use old 8.1, 7 ... just to play LoL.
Riot will probably have to cover this, as it's part of upcoming autumn Windows official update, part of Win 2019 server and in skip ahead (19H1) ring.