A healthy website relationship means a business can leave its current developer or host at any time and take the site with it. Some setups, whether by design or neglect, make that far more difficult than it should be, effectively trapping a business with a provider it may no longer trust or want to work with.
You don't have your own login credentials
If a business owner doesn't have direct login access to their own hosting account, domain registrar, and website admin, and instead has to go through a developer or agency for every change, that's a significant warning sign, not a normal arrangement.
The domain is registered in someone else's name
If the domain, the business's actual web address, is registered under a developer's personal or agency account rather than the business's own, the business doesn't truly control its own domain, regardless of who built the site. See domain renewal: how to avoid losing your own domain.
No usable copy of the site exists anywhere else
If the only copy of a website exists inside one provider's proprietary system, with no way to export a usable version, leaving that provider can mean rebuilding from scratch rather than migrating.
Getting a straight answer about leaving is difficult
A legitimate provider should be able to clearly explain what it would take to move a site elsewhere. Vague, evasive, or discouraging answers to a direct question about migration are worth taking seriously as a signal.
What to do if this describes your current situation
Start by directly requesting full access: hosting login, domain registrar access, and a full export or copy of the website files. A reasonable provider should be able to provide this without much friction. If they can't or won't, that itself is useful information about the relationship.
Questions
Is it normal for a developer to manage hosting on a client's behalf?
Yes, that's a common and reasonable arrangement, as long as the client still has, or can easily get, direct access and ownership of the actual accounts involved, not just a promise that it's being handled.
What should I ask before hiring a new developer or agency?
Ask directly, upfront, who will own the domain and hosting accounts, and what the process looks like if you ever want to move the site elsewhere.
Does a static site make this easier to avoid?
Yes, in part. A static site built from plain source files is inherently more portable, since there's no proprietary database or platform lock-in involved, only the question of who controls the actual domain and hosting accounts.