In practice, it doesn’t work that way. The classes that can remove disease either get it as part of their loadout and can’t change it (Paladins), or there is essentially no cost for them to do so (Clerics and Druids prepare spells, so it costs them a single prepared slot).
Meanwhile, a character that devotes resources to solve this precise issue (some combination of skills, expertise, features or magic) can’t.
For both Mummy Rot and Clay Golems,
@Lanefan and
@Micah Sweet say that the challenge is the point. But if that is the case, let me make a modest proposal.
For Mummy Rot, it is resistant to normal and magical healing. You require Expertise in Medicine and advanced medical tools (so not capable in the brush) to fix it. Until then, a DC 20 Medicine check can stave off the effects for 1 day (or simply give advantage on the roll).
For the Clay Golem, the cause of the max hp reduction is unclear. Say it is from wounds that din’t heal. Use the same principle as for Mummy Rot. You need Expertise in Medicine to fix it permanently , in the meantime, a difficult trained Medicine check can stave off the effects temporarily.
In both cases, a “challenge” DM can tweak the difficulty as wanted.
The only way in which the existing rules are superior is that they preserve the supremacy of magic. Why is that a consideration?