Some of these justify a rebuild on their own. Most do not, and get quoted as one anyway.
Rebuild, usually
It does not work properly on a phone
How to check: You have to pinch and zoom to read a paragraph, the buttons are too small to hit, or the menu does not open. Check on a real phone, not a resized browser window.
The fix: If the theme was built before mobile mattered, retrofitting is usually more expensive than rebuilding. Most of the people finding a local business are on a phone, so this is not a cosmetic issue.
Rebuild
You cannot change anything yourself
How to check: Updating a price, an hour, or a photo requires someone else. The hours on your site have been wrong since a holiday two years ago and it was never worth the phone call.
The fix: This one compounds. Everything about the site drifts out of date because keeping it current has a cost every single time. Rebuild on something you can edit.
Fix, not a rebuild
It is slow, and that is the whole complaint
How to check: Run a speed test. If the problem is oversized images, no caching, or plugin bloat, that is a maintenance job.
The fix: Fix the speed. A new site built without attention to the same issues will be slow too, which is a thing that genuinely happens.
Depends
The design looks dated to you
How to check: Ask whether a customer would notice, or only you. Then ask whether the dated look is costing you calls, or just bothering you. Both are valid, but they justify different budgets.
The fix: A design refresh over the existing structure is often enough and costs meaningfully less. Reserve a full rebuild for when the structure is wrong too.
Rebuild
The structure does not match what you sell now
How to check: You do five things and the site covers two. Or the site is organized around a business you have moved on from. Search visibility follows structure, so this shows up in rankings as well as in confusion.
The fix: Rebuild around what you sell now, one page per service. This is the version of a redesign that reliably pays for itself.
Not a design problem
Nobody visits it
How to check: Analytics show single-digit daily visits. Redesigning will not change that, because the number of people who see the new one is the same number who see this one.
The fix: Search visibility and local listings first. Come back to the redesign question once people are actually arriving.
Fix today
The form does not work
How to check: Submit your own form and see if it arrives. Check the spam folder. Broken forms are startlingly common, and they fail silently, so nobody learns until someone mentions it in person.
The fix: Fix the form now, whatever you decide about the rest. Every day it stays broken is leads going nowhere.