People keep using the power plant analogy as if somehow there isn’t a massive shift towards solar and batteries, which are literally building a power plant on your roof.
No one is really "building" anything when they run their server though; it's all built by hardware vendors, you get the software from software vendors, etc. You're just operating it.
I don't really like using analogies for this sort of thing as I think it muddles things more than it clarifies, and quickly leads to discussions about the analogy rather than the topic at hand, but if we must use one I'd say it's more analogous to a business deciding to purchase a company van or lorry. For a lot of businesses, this clearly isn't needed and renting one when you do is fine, but at some point it just becomes easier and more cost-effective to have your own (depending on what you do with it, nature of your business, etc.) in spite of the extra hassle of having to maintain, clean, etc. your vehicles.