Here, it literally is; typically 4.5x the annual household income is the most the average bank will lend you. There is also a separate affordability test which works the way you describe. https://www.google.com/search?q=uk+mortgage+to+salary+ratio
Sorry, I was talking specifically in the US. I think you may be talking UK.
We have a "front-end" ~28% and "back-end" ~36% debt to income (DTI) limits (typically). Front-end is ratio of mortgage loan to income and back-end is ratio of all debt to income.
The interest rate can wildly change the size of loan you can get for a given income because of this method (as we saw prior to last year).
If you had a fixed ratio, when interest rates go up a 4.5x mortgage would be a lot less affordable. I can't imagine paying a 8% loan on $450,000 with $100,000 income. That's be $4000 a month, front-end rate of ~48%. Ouch! Guaranteed foreclosure.
Neither system is perfect, I still don't like that non-debt expenses are not counted and it should be net income after taxes.
Here, it literally is; typically 4.5x the annual household income is the most the average bank will lend you. There is also a separate affordability test which works the way you describe. https://www.google.com/search?q=uk+mortgage+to+salary+ratio