This is because WordPress.com is unique in this regard.
If you purchase hosting and install WordPress on that host, you can then put a theme or plugins in the relevant folders, hundreds of themes, or even put a completely different application in WordPress’ place if you chose to. This is what’s called a self hosted install in the community.
So you aren’t paying for WordPress, you’re paying for the server that hosts it, and you can put what you like on that server. You could put several WordPress installs on it, or WordPress + Joomla in a subfolder, the decision is yours and dependent on your technical skills time and desires.
WordPress.com however is different. WordPress.com is a commercial service from Automattic, and when you register a site, you’ve created a site on a gigantic multisite install of WordPress. It’s similar to creating a self hosted site then letting people sign up to it and create their own sub-sites. It’s also why you can’t create a multisite on WP.com ( because it’s already a multisite ).
When you pay to install a theme, they migrate your site off of that install and on to its own hosted infrastructure. At which point you can then install themes and plugins just like other hosts. The difference being that you only get access to part of the WP folders and files. This is because they manage WordPress itself.
Think of it as the difference between installing Microsoft Word, vs using Office 365 Word. WordPress.com is “WordPress as a service”, just like Office 365 is Microsoft office as a service. That’s what allows them to let you create websites for free.
Disclaimer: I am a former employee of Automattic, details may have changed. For specifics on how WordPress.com sites using the premium and business plans work please contact WordPress.com support