Yes. But maybe not the way you think.
This section is designed to provide the GM with a tool to enable their overarching responsibilities. Yes, technically, you should follow the rules (and that means checking all your steadings) but the rules of Dungeon World aren't meant to be hard to follow. Keep in mind that you are only checking whether or not the steadings need to be updated based on what is going on in your game world. This rule forces you to think offscreen too in a way that allows you to exploit your prep. It just gives you a list of things to consider before deciding that nothing has happened so you don't ignore consequences that aren't obvious. If nothing that is going on would have affected it, it should be pretty obvious just from glancing at the checklist and campaign fronts.
If you're worried about how much work this going represent, you should consider using a tool such as the campaign map and wiki features of Obsidian Portal to make it easier to update and track. However, also bear in mind that new steadings are added only as the fiction demands it. If you're adding new steadings because you're moving to new territory, that's good. It also means whatever is going on is less likely to have a session-to-session impact on the other territories farther away. However, if the map starts to become over-saturated you have a few approaches you can try.
- Give the players incentives not to create new steadings. This can be anything from the benefits of dealing with NPCs who remember them to running entire Adventure Fronts within a city. Give them a reason to want to return.
- Not every steading needs to be city. Or even a proper village. Something as a small as a lumber camp or well-established farm (homestead) could qualify. The less there is going on, the less you have to worry about when it comes time for the checklist.
- Not every update has to be positive. A natural consequence of over-saturation is a strain on resources. This can cause all sorts of problems, from people leaving for more prosperous locations to war and bandits. This can be fodder for adventures (see point 1) or it can simply mean that a village becomes a ghost town. At that point, you probably don't need to worry about updating it as a Steading. You should absolutely still think offscreen too.
- Dungeon World's mechanics are heavily integrated around a core philosophy that makes it difficult to change rules without unintended consequences. However, it is permissible. Once you've had some experience you may see ways to simplify things without extensive adverse affects. For instance, you might decide that it makes more sense to keep a distinct campaign map for each "region" and only update other regions after a Front resolves or when players are returning to them.†
On a side note, if you're interested in programming something to make this process easier, you might consider mapping the steading relationships so when you change the tags on one the related steadings show up as needing reviewed (in case that change affected them).
† Disclaimer: I haven't tried this before and so it is an example, not a suggestion.