It is possible he plays on without his back in such disarray, but his back problems had been severe and building for awhile. I am amazed he managed to play well enough to be a major contender on 1 surface (hard courts) still in 2004 and 2005, play close to his former best and in some matches (some of the big US Open matches) better than his mid 90s performances where he got struck by nerves in some of those big matches vs Sampras, and really push peak Federer in both their 2004 and 2005 US Open matches. I am sure that is the reason he was useless on both clay and grass by then, after still being strong on both in 2003. I can't imagine there is a scenario he can last much longer.
Furthermore nobody played full time singles tennis until 40 back then. Just wasn't done. In fact most retired barely past 30 like Sampras, Graf, Seles, all did. I am not sure the mindset to play until 40 would have ever existed. He was married to Steffi Graf, they had 2 young growing childen, and his chances of ever winning another major, already slim, would just diminish as he got older, and Federer and others grew only stronger, even at full health.