Just be careful. The free version of wp.com embeds AD-Code and tracking scripts into your page so they can make money. The paid version is without ADs however. If you want privacy, the one-click installs (like you said) on the majority of hosting providers is better.
The free version of Wordpress.com has become gnarly in recent years. They even use a dark pattern to trick you into thinking you have to buy a domain for your blog when in fact you can always just use a wordpress.com sub domain.
Just be careful. The free version of wp.com embeds AD-Code and tracking scripts into your page so they can make money. The paid version is without ADs however. If you want privacy, the one-click installs (like you said) on the majority of hosting providers is better.