. . . there won't be any Bitcoin left as they'll all be lost in millions of accounts with 0.000001 BTC . . .
Well, to start with, if there aren't many bitcoins left, then the value of each remaining bitcoin will be significantly higher. If 0.000001 BTC is worth $1 then the necessary fee to send it will probably end up being lower (perhaps 0.00000001 BTC?).
Regardless, if millions of accounts loose 0.000001 BTC, that really won't be much loss.
Lets assume 100 million accounts all loose 0.000001 BTC. What is the total amount of bitcoins lost in that manner?
100,000,000 X 0.000001 = 100 BTC.
The total amount of bitcoins that will exist is a bit less than 21,000,000.
This means that 100 BTC lost is about 0.0005%