> This begs the question how ticketing/arresting clears the streets [if there are no shelter beds available]? By shoving them elsewhere for another city to ticket?

Driving people elsewhere is one major mechanism.

That can mean to other cities - it's a zero-sum game, but so is buying homeless people bus tickets to leave, and cities do that too.[1] It can also mean pushing them outside city limits into the metro area, or into less-desirable areas with fewer officers and/or informal instructions not to ticket the homeless. (Similarly, arresting homeless people isn't meant to house them in jail, but to get them out of heavily-policed areas.)

[1] https://www.nytimes.com/2019/09/14/us/homeless-busing-seattl...