It would be much smarter to ask developers to change something in the way aggregate groups are presented, by not loading so much contents. It should work mostly like categories indexing pages, and allow easier selection by focusing to a group of interest without mixing everything on the same page (this is not sustainable and it is really a challenge to have the translation framework scale up to support large much larger wikis).
This has been already requested since long, but progresses for the Translation extension are extremely slow (much slower than the current growth of translated pages). It is already a huge problem for using it on small devices, but even with modern browsers on fast PCs, we are still constrained by the data volume generated by these pages, and the restricted memory in browsers (most of them are still 32-bit, including on 64-bit systems, due to their javascript engine, CSS engine, and DOM processor).
We've already passed since long the size that would cause normal wiki pages to be signaled for excessive size.
Disabling groups is just a poor solution. Cast your vote and send your opinion in Bugzilla to support this development.