So if "most" means 90% (which is very charitable compared to the real world) this still leaves 1,000,000,000,000 x 10% = 100,000,000,000 undesired mutations. I don't think this math is so very hard. It might be harder if one couldn't afford to be off-the-top-of-one's-head charitable and had to quibble over which estimates to use. That's not the case. One can afford this luxury and more.

The mutations that aren't eliminated spread throughout the population. How many steps backward can one take for every step forward and still make progress? Even if the population only accumulated 2 bad mutations for every good mutation, extinction clearly must result; and it doesn't take a billion years either.