The apartment I used to live at only wanted a $500 deposit - rent was around $3300/month. This was an apartment complex owned by a large company (Equity Residential) so honestly it confused me as I thought they'd try to squeeze as much money as possible from tenants. They did that for rent increases - the increases were always the maximum allowed by law (5% + CPI, capped at 10%), down to the cent.
2 months is pretty typical, and 1 is not long enough to cover the cost of an eviction.
If you prevent landlords from taking a deposit big enough to cover the real cost of a bad tenant, they will protect themselves by discriminating against rental applicants.