First up you get Shards every time you level, every 25 levels is a milestone and provides extra swag thou the extend of this currently remains to be seen. So you can 1 trick and still get BE, your standard hex tech loot remains unchanged. A trick I have used for chests is to que with a buddy whos on a main champion and can reliably get S ranked to unlock chests on any off champion your playing thru the que benefits, this will help minimize the time your not playing a main and maximize down time on chest CDs and free loot.
Far as games to hit level 100, its possible to pull that off with something like 700 games over the year. I think the worst case BE drops from level gains puts one at roughly 9 levels to unlock new champions, which should be pretty easy to do over 45 days so its fairly similar to previous IP grind rate. I'm doing the math fairly loosely here and biasing a lot of my numbers off the worst case, low BE shards and High account level.
Personally I leveled up in 2 days and so I would see enough BE at about 18 days as this pace to unlock a new 6300 champion I did not have a shard for. Only I did not get the worst case shard and had about 900 BE value from my level up so if that trend sticks only takes me 14 days, at the rate of 2 games per day. As you can see the amount of games folks play to level will vary quite a bit.
If you spend all year playing casually and hit that level 100 you have enough essence to buy only 7 ish new champions, which is not much if you don't own champions but theres other options on how add content to your account. The plus is if your maxed account you will have a pretty easy time keeping up with releases. For newer level 30 accounts they have options, fill in blank spots via upgrading shards they get thru RNG for a discount, and mystery champion which cuts down the cost of champion almost in half once your eliminate the RNG of lower cost champions out of it, or still generate enough BE as an older account to exclusively purchase 7 champions they absolutely must have.
So still will take accounts over a year or So to unlock all content but that's business as normal in league. I recall it took me 2+ years to finally own all champions and have a decent set of runes. If you need to speed it up cave and throw the RP at them, but the slow grind for all champions remains the same and is a substantial commitment of time just like it has been for years.
I hope that was helpful to you and please let me know if you have any questions or are unclear, I'm about to crash for the night but I will follow up if you need further help when I get home from my shift tomorrow. Night mate and be well.