How to avoid branchageddon with large organisations?
As Michael mentioned, offer a standard solution based on release versions/numbers, with a reasonably long lifespan for your industry (maybe interleaved with one or more shorter lifespan intermediate versions, if it makes sense for your typical customers).

Give your customers the option to embark on this standard release track, maybe with a decent migration deadline in place.

If they insist on a full-custom branch support strategy just charge them accordingly, to properly cover all your extra costs for offering such full-custom support - it only makes business sense. Some customers will migrate to reduce their costs (which will help you reduce the number of custom branches), some won't. 

Variable support billing, growing progressively with the age of the release versions from which the custom branches originate can also be an incentive for customers to migrate to newer branches faster, helping with faster closing of the older custom branches. This can help reduce the number of custom branches per customer - if you have customers that simultaneouly run multiple versions of your software.

Make sure you don't fall into the trap of doing full branch merges from/to any of the release branches (both standard and custom), all changes to them should be either individually developed or cherry-picked merged fixes. 

Because each of these branches will gradually diverge from each-other, the number of hotfixes requiring customisation/individual development will grow exponentially (plain cherry-pick merging will fail). You need to take the development cost for these into account.

With no (significant) branch merges in the picture you can (and should, I cannot stress its importance enough) build fully automated CI/CD pipelines for these branches, accompanied with a good hotfix tracking/management system in place, making the hotfix delivery just routine (or almost).