Do you really have that many coworkers that people are pushing every few seconds on the same branch?

Yes, during the work day, many people would like to commit their changes, often during the same timeframe. Every step takes a second or two, so there's plenty of room to get conflicts (I moved closer to the git server, so now I have an advantage!)

CVS was nice(ish) since changes were independent, any number of people could check in code to limit of io parallelism. Svn was nice, the server would wait for a lock and if my changes didn't conflict, they would be applied after the rest of the pending commits. Git is a PITA, large companies build elaborate systems to queue commits, but we're not big enough to use that yet.

Does everyone in your company push to master all the time? Or is it different PRs being merged all the time?

Pretty much yes. We like to push to master, and then push to production. Some teams cherry pick changes to a deployment branch and deploy from there instead of master.

Edit to add: We may be "doing it wrong", but this is the least effort way to do centralized development.

No seriously, consider git branches. It's gotten 100x easier to create, manage, and merge branch pull requests. Most projects I join these days in fact "lock" master and you are forced to develop in branches.