The main issue with an LTS is that there's no such thing as "long enough". Upgrading once every three years -- especially when the compatibility policy now is that if you run on the previous LTS with no deprecation warnings, you'll also be able to run on the next LTS without errors -- is not that much of a burden. But many organizations won't put in the time to do the upgrade until it's too late, and the length of the support period doesn't actually matter: an organization that can't manage an upgrade in 3 years also won't manage an upgrade in 5 years, or even 10 years, because the problem is not that the support period was too short. The problem is the organization's priorities, specifically the fact that doing maintenance work is not a priority.
A good example is Python 3 support. Python 3 was first released 11 years ago, and Django introduced support 6.5 years ago once Python 3.2/3.3 stabilized a lot of things. But there are still people today who haven't even *started* to upgrade to Python 3. It wouldn't matter if we gave them a hundred years -- it still wouldn't be "enough time" for them to upgrade.
I understand the arguments for *why* organizations do this -- which mostly come down to "it works right now, why should we spend time on something that isn't broken when we have real bugs to fix and features to add?" -- but unfortunately they usually end up learning, when it's too late, why they should have made time for maintenance work earlier. Giving them a longer support period won't change this. And a 3-year support period is a reasonable amount of time, especially given the work being done to make the LTS-to-LTS upgrade easy, and doesn't overburden the Django team with having to support ancient versions of the framework until the end of time.
With that said, there are Linux distributions which provide their own packaged version of Django, and which have longer support periods in which they will backport important fixes into their package even if the Django team isn't supporting that version anymore. Some of them charge money for this service, but if you need to buy a couple more years of support for an old version of Django, using one of those distributions may be your best option.