How about if you have set aside four hours for a literature review, and you use LLM assistance in the first hour to narrow down the best options for things to spend the next three hours diving deeper into?
LLMs can help with those early reads and save some time and get you into the deep reading sooner with more context. If during the deep reading you would normally jump back to a previous section to check something, it's likely faster and easier to just have a conversation with the paper (enabled with an LLM). The same would be true for that final read where you're doing logical checks.
If you use an LLM to give you a summary and leave it at that, you'll have done the equivalent of the first pass through a paper. That could be enough for you to know you want to filter it out and not do a deep reading, but you'll lose the benefits of the deeper reading. It seems like there are clear benefits and areas where LLMs can help improve that current paper reading process but if you skip (instead of just replacing with a more efficient LLM alternative) major parts of that process you'll get less out of it than you would without skipping those steps.