William Hartnell wasn't particularly old -- he was 55 when he got the part and was made up (with a white wig, etc.) to make him look older -- but his health gave out after a few years (partly because of the demands of a series that gave hin only a couple of weeks' holiday a year).
When the show started, the BBC expected it to last only a year or two and the idea of regeneration, allowing the lead role to be played by a succession of different actors, had not been thought of, so they didn't think of him as "the original Doctor" but as "the only Doctor". It was, in fact, because of Hartnell's failing health that regeneration was invented and it's because the Doctor can regenerate that the show has lasted this long.
If the BBC had cast someone whose health had turned out to be better, the show might have ended long ago, so we ought to be grateful they didn't.