I understand you wouldn't want this to be the default, particularly for people who have one giant running session for many topics - and I can only imagine the load involved in full cache misses at scale. But there are other use cases where this thinking is critical - for instance, a session for a large refactor or a devops/operations use case consolidating numerous issue reports and external findings over time, where the periodic thinking was actually critical to how the session evolved.
For example, if N-4 was a massive dump of some relevant, some irrelevant material (say, investigating for patterns in a massive set of data, but prompted to be concise in output), then N-4's thinking might have been critical to N-2 not getting over-fixated on that dump from N-4. I'd consider it mission-critical, and pay a premium, when resuming an N some hours later to avoid pitfalls just as N-2 avoided those pitfalls.
Could we have an "ultraresume" that, similar to ultrathink, would let a user indicate they want to watch Return of the (Thin)king: Extended Edition?