It costs engineering time to do so. Time that could otherwise be used to build features, better protect against more common failures, attract users, etc.

Amazon probably has ~5hrs/year of complete failure of a region. Figure, conservatively, it would take 3 months of engineering time to protect against that, plus a 'continuing' cost of 1/2 a week per month to maintain that protection. You'd also have to (at least) double your provisioned capacity (which may include a larger ops team, etc). Assuming your servers cost $20k/month and devs cost $100/hr (both fully loaded), we're talking about ~$340,000 to prevent 5 hours of downtime (just for the first year).

If downtime costs you more than $50K/hr, then it might make sense to be that fault tolerant. Otherwise, there might be better places for a startup to spend its (limited) resources.