No, it's throwing good money after bad.
First, I wouldn't really call a 350 a modern CPU. It lacks some of the instructions of the other newer DL CPU's like the 250/260, the 450, and the 05/06, even though all of those have been greatly, greatly surpassed by the Do-More. I had a customer where I'd installed several copies of an app written on a 250. They had one PC-controlled machine that used a 305-classic as I/O, so I thought to load my app by switching out the CPU to a 350. No dice, had to rewrite it.
In the meantime, all the I/O is old. If you, either proactively or gradually as they die, replace them, now you have all new I/O, but you've spent the money that could have bought you a brand new PLC. Then, 305 racks have some issue where they die after about 10 years. I haven't experienced this with any other rack-based PLC I've used or seen.
For equipment you're going to junk in the foreseeable future, I'd agree with you, just replace parts as they fail till you're ready to decommission the machines. If you don't have a horizon in sight, bite the bullet and put in something that has far more capability and will continue to be available far longer.
I have yet another customer with a piece of equipment running on a 20-year old SLC with Flex I/O. They recently priced a new CPU (32K 5/05), and it was $7,000!! Just the CPU! A brand new S7-1500, that's probably 100 times the PLC and will continue to be available for years would cost about half that, INCLUDING the I/O. A Do-More, probably half of THAT.