That's fair criticism. Let me rephrase the assumption: Can we assume that the same fundamental laws of physics are operating today as were operating in the past? If the laws of physics have changed, then yes, everything is out the window.

If fundamental physical laws have not changed, then we can use what we know about present-day physics and chemistry to constrain what events occurred and what processes were operating in the past. This is geology in a nutshell.

For example, you cannot produce the type of quartz overgrowths and cements observed there and many other places at near surface conditions (i.e. the processes that make sand a sandstone similar to the ones in that outcrop). The reaction requires higher temperatures, higher pressures and different fluids to reproduce experimentally.

So either the rocks weren't at the surface, or the surface of the planet was be pressurized to hundreds of times atmospheric pressure and and bathed in very hot, very reactive fluids.

Next, there are minerals in the sand and mud that had to be weathered and transported at surface conditions. If the surface conditions were dramatically different than today, the minerals we see would be unstable and would quickly change to a different mineral. (They can change back and forth, but you'd see pseudomorphs and other evidence of that happening.)

That puts constraints on the temperature and pressure of the Earth's surface in the past. It implies that the rocks started out at conditions not too different from today's surface, and then were subjected to conditions very different from today's surface.

Lets say the rocks were heated up in a giant kiln. You're dealing with a kilometer thick section of rock that's thousands of kilometers wide that has all experienced similar conditions. If the laws of physics are the same, we can calculate how long it would take to get the rocks from surface conditions to equilibrium at the necessary temperatures. Circulating hot fluids through the rock can speed this up by 1-2 orders of magnitude. It's still not particularly fast. Thousands of years at the minimum, and that's pushing things (rocks are good insulators -- they don't conduct heat well).

Next, the only non-supernatural way we know to get the rocks to those temperatures and pressures is to bury them beneath other rocks. That takes time, even if it's far more rapid than what we see today. You then need to exhume them back to the surface, which also takes time.

That outcrop is showing two complete cycles of the processes outlined above, with a third in progress. That's the point Hutton was trying to get across with that particular example. It's not even that there's slow deposition, etc, it's that there's evidence for multiple cycles of things that have to take a long time. The chemical reaction-based argument I made above is a bit different than what Hutton argued, but it's the same basic idea.

This is not to say that things are purely slow gradual processes and no unique or extreme events are recorded

The geologic record is actually dominated by extreme events.

For most rocks, what you see is not evidence of constant gradual deposition, but pulses of deposition. The rock record is mostly gaps. Most sedimentary rocks are actually records of extreme events like hurricanes and floods. Volcaniclastic rocks are records of volcanic eruptions (again, extreme events). The processes that shape the Earth are localized in space and time.

Also, there are several examples of rocks in the geologic record that could never have formed today. (e.g. search for komatiites) We don't need exactly the same processes to be in operation, we just need the same physical laws. The rest can be derived.

Finally, yes, we do frequently use modern environments as analogues. It's not circular reasoning to do so. You do need to be keenly aware of the potential for differences, but it's more akin to a large-scale experiment than a strict "this must be exactly what happened in the past". The time and spatial scales often make traditional experimental methods impractical, so we use modern analogues in those cases. The question asked when using a modern analogue is not "what is happening here", but rather "what underlying physical processes are responsible"? The goal is to constrain the parts that can't change or are unlikely to have changed.