While you can still do what you did, likely you wouldn't have a static IP - at least not here in the United States.
Most home connections have a dynamic IP provided by DHCP; now, usually, that IP won't change (probably tied to the MAC address of the modem or router) - but it can change. So what most routers provide is a way to report the IP to a service like "Dynamic DNS" (https://dyn.com/dns/ - which used to be free, and this is first I've learned that it's now an Oracle project - sigh) - which can then be pointed to as the DNS service for the site - so if your address ever changes, name resolution will still be available. Other settings in your router can do various other functions to route the traffic to-and-from your server.
Which is where it also gets tricky.
Most providers "look the other way" when it comes to servers, provided they don't get popular. They also block more than a few ports, so you have to work around that as well (mainly standard ports like 80, 25, etc). But technically, most TOS contracts with broadband ISPs forbid the running of servers, and they can pull your connection if they want to for that TOS violation.
The other option would be to sign up for "business class" service with an ISP. Sometimes you can get this with your current home ISP - for a massively inflated price (and usually a drop in speed if you want to keep the costs the same). But usually you are given one or more static IPs, and the ability to run servers is part of the deal. Not all home ISPs provide this service, but the big names (COX, Comcast, etc) I believe all do.
Some, though, might throw in another "catch": You can't have business service to a residential address. This will vary based on your provider; most have realized the idea of SOHO setups and the need/want for business class service for these home-based systems. But not all have. So you have to keep that in mind, as well.
Which is why, instead of going thru all of that hassle (and it really isn't a minor amount - on top of everything else you have to do to run a home-based server, plus security, etc) - most people will instead go with some other hosted solution, a cloud virtual server being the first choice for most today.
Shared hosting is still available, of course, but last I checked, you can't get use a letsencrypt certificate with these, depending on how they have things set up (you can still purchase and set up your own certificate - but that's more money out the door).
Colocation is still an option - but it tends to be (always has been) an expensive proposition for most, unless you're planning on using it for a small amount of shared hosting (friends and family?), or you run a business providing such hosting as part of a package (I worked for an employer who did this for his clients as part of the custom websites we built - but if they wanted to host it themselves or with another provider, that was an option). Or it might be that for certain needs it would be cheaper to build the server yourself and colo it, than trying to use virtual or cloud hosting for a similar system (or you want more control over the system - the ability to visit the data center to upgrade or fix issues can be useful).
So there are plenty of options out there for someone who want to run their own piece of the internet. Ultimately, though, aside from cloud virtual hosting services, they all require a fair amount of technical competence that keeps most away, and even those who have the knowledge sometimes don't want the administrative and maintenance headaches that come with the territory.
That can be true to an extent even with shared hosting. For instance, I personally have an old shared hosting account with Hurricane Electric; I was running a website using PHP and MySQL, and about a year ago (or maybe it's been longer?) they upgraded their servers to a new version of PHP that ended up breaking my website something horrible (my website was originally a way for me to learn PHP years ago, and it never got the love it needed ultimately). I put up a quick "site broken - sorry" page and left it.
But the truth is, I don't want to have to maintain even that; worrying about issues with PHP and MySQL, dealing with thoughts of potential attacks, making sure my stuff is secure, etc. For my site, for what I used it for, all that is a hassle. Which is why I have been thinking (but have yet to execute) about going back to a simple static site. If I need comments or discussion (which I don't know if that is necessary), then I can rig up something with an outside provider - but ultimately, my pages should just be simple static HTML and some javascript. Some basic CSS to make things a little responsive, and nothing else much. I've been giving thought to doing this on a DO droplet; it'd be much cheaper than my HE hosting, and give me a bit more freedom (plus I can use an LE certificate).
I think all of this is what holds people back, and makes them seek other simpler paths; they just want to get something up and shown to the world, they don't want to deal with all the technical issues, they don't want to have to worry about security, and they don't want to have to deal with other complexities. This is why sites like Medium, and other providers (QIX, etc) have been so successful; they have removed such strain from the equation. Of course, it has come with more than a few visible, and at times hidden, costs, that content creators (and users) are beginning to experience, and more importantly, understand what they have given up.
We're probably in the process - or right on the edge - of yet another shift in "content hosting" for lack of a better term. Between the censoring on platforms, and other reasons, there is some shuffling going on it seems. What I honestly hope comes out of this is a move to distributed content (so-called "distributed web", for instance) - but I don't think things are quite there for people to really use it (though some distributed platforms I have seen really seem to be right on the cusp for adoption - if they can just market it right).