Pretty interesting.  You're still constrained by your ability to specify solutions, so you can't immediately solve cold fusion or FTL (you'd need to manually write and debug an accurate-enough physics simulator first).  Truly, no computing system can free you from the burden of clarifying your ideas.  But this constraint does leave some scope for miracles, and I want to talk about one technique in particular: program search.

Program Search

Program search is a very powerful, but dangerous and ethically dubious, way to exploit unbounded compute.  Start with a set of test cases, then generate all programs of length less than 100 megabytes (or whatever) and return the shortest, fastest one that passes all the test cases.  Both constraints are important: "shortest" prevents the optimizer from returning a hash table that memorizes all possible inputs, and "fastest" prevents it from relying on the unusual nature of the oracle universe (note that you will need a perfect emulator in order to find out which program is fastest, since wall-clock time measurements in the oracle's universe might be ineffective or misleading).  In a narrow sense, this is the perfect compiler: you tell it what kind of program you want, and it gives you exactly what you asked for.

Risks

There are some practical dangers.  In Python or C, for example, the space of all programs includes programs which can corrupt or mislead your test harness.  The ideal language for this task has no runtime flexibility or ambiguity whatsoever; Haskell might work.  But that still leaves you at the mercy of God's Haskell implementation: we can assume that He introduced no new bugs, but He might have faithfully replicated an existing bug in the reference Haskell compiler, which your enumeration will surely find.  This is unlikely to cause serious problems (at least at first), but it means you have to cross-check the output of whatever program the oracle finds for you.

More insidiously, some the programs that we run during the search might instantiate conscious minds, or otherwise be morally relevant.  If that seems unlikely, ask yourself: are you totally sure it's impossible to simulate a suffering human brain in 100 megs of Haskell?  This risk can be limited somewhat, for example by running the programs in order from smallest to largest, but is hard to rule out entirely.

Applications

If you're willing to put up with all that, the benefits are enormous.  All ML applications can be optimized this way: just find the program that scores above some threshold on your metric, given your other constraints (if you have a lot of data you might be able to use the best-scoring program, but in small-data regimes the smallest, fastest program might still just be a hash table.  Maybe score your programs by how much simpler than the training data they are?).

With a little more work, it should be possible to -- almost -- solve all of mathematics: to create an oracle which, given a formal system, can tell you whether any given statement can proved within that system and, if so, whether it can be proved true or false (or both)...that is, for proofs up to some ridiculous but finite length.  I think you will have to invent your own proof language for this; the existing ones are all designed around complexity limitations that don't apply to you.  Make sure your language isn't Turing complete, to limit the risk of moral catastrophe.  Once you have that, you can just generate all possible proofs and then check whether the one you want is present or not.

Simulation

Up until now we've been limited by our ability to specify the solution we want.  We can write test cases and generate a program which fulfills them, but it won't do anything we didn't explicitly ask for.  We can find the ideal classifier for a set of images, but we first have to find those images out in the real world somewhere, and the power of our classifier is bounded by the number of images we can find.

If we can specify precise rules for a simulation, and a goal within that simulation, most of that constraint disappears.  For example, to find the strongest Go-playing program, we can instantiate all possible Go-playing programs and have them compete until there's an unambiguous winner; we don't need any game records from human players.  The same trick works for everything simulatable: Starcraft, Magic: the Gathering, piloting fighter jets, you name it.  If you don't want to use the oracle to directly generate a strong AI, you can instead develop accurate-enough simulations of the real-world, and then use the oracle to develop effective agents within those simulations.

Endgame

Ultimately the idea would be to develop a computer model of the laws physics that's as correct and complete as our computer model of the rules of Go, so that you can finally develop nanofactories, anti-aging drugs, and things like that.  I don't see how to do it, but it's the only prize worth playing for.  At this point it becomes very important to be able prove the Friendliness of every candidate program; use the math oracle you built earlier to develop a framework for that before moving forward.

I suppose I would test out the claim by getting it to mine a few hundred $million of bitcoin for me.

Then crack all the interesting crypto data that is floating around. 

Then brute force search for proofs/solutions of all the big problems such as Riemann Hypothesis, factoring etc. Try all texts shorter than say 100 terabytes and see if they solved the problem.

Work out the implications of all the human genes by calculating out how the human body works. This would include things like solving protein folding.

Find the best/shortest algorithm for all the AI/ML challenges that delivers near perfect results. 

Then simulate the body with various chemical compounds added to cure cancer, infections etc. Design vaccine + cure for coronavirusV2 and also machines to make them.

I guess you could create a model of the brain and then run all sorts of experiments on the simulation to work out how it works. 

Simulate atoms and molecules and brute force ways to build things that would build arbitrary nanotech engines.

At what point would you get worried about AI safety?

You could probably make drastic improvements in AI, because you could do extremely expensive things like modeling any function by minimizing its Kolmogorov complexity. I bet you could develop superhuman AI within a day, if given access to a computer with 2^2^100 clock speed.