It's a difficult one. We all want a bit of consistency in our Doctors and we all want the actor playing the part to stick around as long as possible. The problem for Capaldi is that his incarnation hasn't clicked with the public; argue the toss as much as you like, bandy around (falling) AI figures, ratings etc, he just hasn't. I feel for the actor who is, of course a lifelong fan who now finds himself in his dream role and it's just not working properly. The fault must lie with Moffat who has utterly fudged the twelfth incarnation and finally chased away those last casual viewers who had hung on post-Tennant (even though they weren't much enamoured of Smith but they stuck around out of a lingering residual affection for the show built up across the spectacularly-successful and inclusive RTD seasons). An older Doctor was always going to be a difficult sell post-Tennant and Smith and when the signs appeared in season eight that the audience weren't buying it, Moffat and co panicked and tried to rewrite Capaldi into a "younger" version of himself for season nine by virtue of terrible gimmicks such as hoodies, guitars, silly catchphrases and an altogether more juvenile persona. Moffat resorted to his misguided "madman in a box" view of the Doctor(which has always been wrong, imo - the Doctor has always been the one who palpably ISN'T mad) because his bag of tricks was exhausted by around the end of season 5. But Moffat has the 'Sherlock' trump card so in many ways the BBC have allowed DW to become a sacrificial lamb at Sherlock's altar; Sherlock is a huge hit, has popular acclaim...DW is no longer the new kid on the block, it can just trundle along on its own for a while. If it wasn't for Sherlock, i suspect the BBC would have moved Moffat along a few years ago - but Sherlock is now more important so they've left him where he is and where he's continued to do terrible damage to the DW brand by completely misunderstanding it and trivialising it.
DW is NOT as popular as it was five years ago. It just isn't. That's to be expected, though, to an extent - long-running shows suffer dips and troughs. But Capaldi hasn't worked. None of my non-fan friends and acquaintances, nor people I meet here and there, watch the show now. It's become "too complicated" and the Doctor is now "too old." i can't imagine these aren't views held right across the country and beyond.
DW desperately needs a fresh start under Chibnall; it needs to "do a 2005" again to entice viewers back. Keeping Capaldi around is unlikely to do it unless Chibnall has got something spectacularly-imaginative up his sleeve (he may well have - Moffat never did). FWIW I like Capaldi as an actor but his Doctor has never caught fire - if he'd had more dialogue like we've seen in the brief 'Class' trailer (and far better stories generally, as well as a warmer and more believable companion character) he'd have had a much better shot at being a fuller, rounder much more interesting figure than the act-your-age clown he's been allowed to become of late. But for the show to thrive in its new era it needs a new face in the titles. Anything less is going to drag the show down before it has a chance to re-establish its credentials and take away the bitter taste of the last six years.