Why wouldn't you? Most websites run on some sort of database. Technology can fail, especially when facing a higher load than expected but generally relational databases are among the most mature technologies in computing.
Removing technical dependencies to avoid such problems is throwing the baby out with the bathwater.
Besides, WordPress is dead simple to set up on almost any shared hosting plan. The static blogging solutions you probably have in mind for the most part aren't.
There's a pretty massive difference in the amount of effort needed to publish a post with either of those approaches vs. just typing it into the WYSIWYG editor on WordPress. If your time is worth $60/hour then you're looking at around ~$10/post in additional time spent. You also lose a bunch of features: comments, trackbacks, RSS, etc.
Git commit and push takes a minute or two tops I fail to see how that is less efficient than clicking save in a WYIWYG editor. The setup time between the two options is probably very similar.
Removing technical dependencies to avoid such problems is throwing the baby out with the bathwater.
Besides, WordPress is dead simple to set up on almost any shared hosting plan. The static blogging solutions you probably have in mind for the most part aren't.