It's also possible that they could not justify the purchase of a new home financially. To replace what they have now in terms of what they own and where it is located would take just too much money. Even if they could find a piece of land someplace on which to replicate the type of home they have now but in a setting just as nice or even better than what they have now, the land cost itself would likely be prohibitive - depending on how long they have lived where they are and how much that current home might have appreciate in value.
When they factor in the land development, water and sewer connection fees, impact fees, and construction costs for a replacement home, it would run much more than what they could get from the sale of their current home. It would take a tremendous amount of personal savings to offset the difference in price or to keep the equity exchange comparable. Very likely they could not get the same size home they have now, or one with the features similar to what they have now, as a replacement due to the higher costs of construction and regulatory compliance compared to what they have now.
So, they can't simply trade their current home for a new home in a different location due to the financial disparity involved. If they were to look for an existing home to replace what they have now, they likely would find one that needed a significant amount of improvements to meet their current needs or one that already was considerably more expensive than what they paid for their current home - and roughly what they could realize through the sale of it.
Another huge reason that people stay where they are is that it would just take too much effort to move. They have amassed so many possession - so much stuff - over the years of living in that home (added to what they already had prior to moving into it), that it would be a monumental task to pack up everything and move. The thoughts of sorting through everything and ridding themselves of excess or unnecessary items just seems more than they are willing to commit to and undertake. So, they stay where they are.
Still (yet) another reason that many people remain living where they are as they age is that they refuse to look at anything else. They are those people who love to look for new homes - on their own or with a professional - and those who don't enjoy looking at properties at all. Their current home may not be that ideal for them, or it could meet their needs in many respects, but they simply don't want to look at anything else. The quality of their current home is not the issue - looking at something else is.
Rather than shop for a new or newer home, or even identify what they would like to have in another home, some people will choose just to stay where they are and never even consider that they could have something else - even if it was feasible for them to get it. They may or may not need improvements to their present home to help them age-in-place more effectively, but they definitely are not considering any other home as an alternative to what they have now.