This has not been my experience, as I've seen many-decade old suburbs continue to thrive thanks to not being so short-sighted to promote extreme density. The ability to continually rebuild/improve with continual turnover is a great benefit compared to often decaying urban sectors missing replenishment.
The Texas model has been to keep growing to the point where the old suburbs are now practically just part of their city.
Richardson (home of Texas Instruments) is literally* just another part of downtown Dallas now. In another decade, Oklahoma City will just be the newest suburb of Dallas.
