How many days is "adequate" to enjoy a driving tour of Cornwall for a group that just wants to see the pretty scenery (no special place we MUST see)? We have two weeks starting October 7th and we'd originally planned to take the train to Penzance on the 8th and use Penzance as a base for 4 or 5 days before taking our rental car and heading out for another TBD Cornwall destination. Now we're wondering if one week is really enough and that we should use the second week to see some of the London-adjacent sites we've never been to such as Blenheim Palace and Kew Gardens. "Adequate" is, of course, subjective, but anyone have thoughts?

I could happily spend a month wandering round Cornwall but of course reality stops that happening and my longest stay in one stretch has been six days. I've also enjoyed a couple of weekends there. It is a very compact county, easy to get around once you are down there (the drive down is not a great road) and you can see a good variety of Cornish landscapes and places in a week. Different areas do vary quite wildly - you can be driving through a pleasant wooded valley at one moment and come out on to desolate heathland the next. So have fun and make the most of whatever time you do spend there.

I would go for a week, personally.
And, to me one of the "Must-see" destinations in that general regional is Tintagel Castle. It is gorgeous , magical and unique. ... and probably one of my most memorable visits while in England.

You could spend a few days on the Scilly Isles.

Although Cornwall is quite compact, if you stay at one end [eg Penzance] it will be difficult to see the other. On the other hand, if you stay in the middle, you'll spend a lot of time travelling.
I would suggest 4 days in Penzance, and another 4 days either in the north of the county [to see the Eden Project, Padstow, Tintagel etc], &/or in Plymouth, so you can explore the south -east.
There is another thread at the moment giving a travel report for this area by train, which may interest you.
In october, you could leave your decision to whilst you are here - you would be able to book accommodation in or around London from Cornwall if that's what you decide you want to do and you would certainly be able to find somewhere to stay in Cornwall without booking at that time of year.
If you have any more specific questions I'll try to answer them - though as I live here, I don't necessarily know what tourists want to know!

3 days near Penzance, 3 days in or near Padstow, and make sure you take your time when going through Plymouth - up to the Hoe and so on, great views and a nice town down by the "Barbican" harbour.