Stripe is a payment processor who likely realized that the only way to get their customers on a modern TLS implementation is to make it extremely obvious they need to upgrade. TLS 1.2 is not the only criteria for a good software platform, it also needs to continue to get security updates and support. For Ubuntu, 14.04 or older is overdue for an upgrade.
As administrator, it is your job to accomplish such an upgrade. Test upgrades versus rebuilds in your environments. Customize an upgrade project to fit your needs.
Try it yourself. Read documentation on upgrading the OS. Upgrade the test servers. Try your applications.
General purpose OS distributions have experienced quite a bit of change in the past 10 years. Including Linux based, who constantly seem to be replacing components. In theory there is an upgrade path to keep the same OS instance, but in reality there will be tricky steps. Perhaps multiple tricky steps, due to the upgrade tools and software dependencies. Some paths may not be supported at all.
So if a new install is easier in the end, why not make one big leap and be up to date for a while? Ubuntu 20.04 is just out, new versions of things and several years of security updates.