Warp capabilities are shown for the various ships. That's a major component of exploration.
Not necessarily, I think. High warp is mainly important if you need to get to faraway places fast.
But there are somewhere between 100,000,000,000 and 400,000,000,000 star systems to be explored in our galaxy alone, a staggering number.
Take the following analogy.
Suppose the largest global sociological survey ever is undertaken - every settlement on earth with 10 people or more is to be mapped, its members interviewed, and the sociological structure of every settlement must be described and analyzed in documents. There are a 1000 teams and they have a go at it.
After a decade, they gather again and conclude only 5% of the task has been completed, as there are so many settlements and recording the internal sociological organisation of every settlement simply takes time - it means staying at each settlement for a few days or perhaps even weeks.
When faced with this kind of 'mapping task', how relevant do you think it is nearly any specific place on earth could potentially be reached within 24 hours by planes and helicopters? I'd say it has become fairly insignificant. The problem is not getting to any single particular spot fast, the problem is getting to all the spots (which there are incredibly many of) (and perhaps even finding them in the first place) and each and every one requires a significant investment of time to explore and document properly up close.
This is only an analogy, of course. We don't know what 'exploration' involves exactly, in the Starfleet sense of the word.
Still, I think it's very possible that having an amazing sensor suite on board is far more important to 'efficient exploration' than having very high warp capability.
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