You can always run a Drupal site somewhere without Aegir. However, as an application life-cycle manager (ALM) platform as a service (PaaS), Aegir adds extra value (e.g. monitoring, backups, rollback on upgrades, etc.)
The value of Aegir increases with the number of sites hosted. The selling point for me is that you can upgrade 200 sites at once with a single button click. But if you only have one site, it may not be worth it. You have to weigh the benefits that Aegir provides (see the docs) vs. the added maintenance of maintaining Aegir itself.
That is, if you really want to run your own platform as a service (PaaS). Other options are hosted Aegir (if you really like it) or finding a Drupal hosting company which offers their own proprietary PaaS for running Drupal. (I'll leave this search as an exercise to the reader. Ask good questions like: Does your Drupal hosting company lack native Composer support?)
Obviously, you can forget about the PaaS, and just run the Drupal site yourself if you want to self host.
If you'd like to try Aegir locally, have a look at the Aegir Development VM.