You might be surprised the limited extent to which this is true. In many places in the US starting residence requires 3x rent (first, last, deposit) and vacancy rates are low. Getting the deposit back from the previous landlord routinely takes months and while legal assistance can usually expedite this it's hard to find (the public law clinic and the law school clinic are running on waitlists), so deposit return doesn't help like you might think. Public assistance in this area is quite limited and may adversely impact the ability to find housing on its own. And the impact of vacancy rates can't be underestimated... in this city it's currently hard to find anything on the low end with a move-in date within weeks, which often requires a very costly bridge stay in a hotel.
As a volunteer I work with a lot of people who have lost housing due to non-financial circumstances (typically fire) and are unable to afford to obtain housing at the same rent due to the up-front expenses involved. The Catholic Charities or city housing authority are sometimes able to front them last and deposit, but both have a limited budget so it runs on a lottery with a low % chance and landlords often find out the source of these funds and then refuse housing (discrimination based on source of funds is illegal in some states but not this one). Charities can cover hotel stay for usually 4-5 days but not much past that point which is not sufficient to cover the gap until a vacancy much of the time. Our case workers routinely watch people go from losing housing due to circumstances beyond their control to homelessness over the course of 2-3 months as they exhaust both assistance and their own funds covering a hotel while trying to find anything they can move into.
When it comes to move-ins, it's certainly not going to be Jeff Bezos but rent is going up significantly right now and so the landlord almost certainly will replace the tenant with someone who is paying more - often significantly more, I've seen 20% jumps from tenant to tenant. Much like switching jobs in the software industry greatly accelerates your pay raises, switching tenants greatly accelerates the rent raises for landlords in tight markets. Most of the US is a tight market right now.