i actually got peripherally involved in some of the design discussions for a Mars polar lander with an ice probe. Unfortunately, this was in the midst of the anti-nuclear phase at NASA and the damn thing would have had to be run by a solar sail the size off a billboard (and with significant katabatic winds on the pole cap, this was a major mission risk).

Anyway, the important observation I made is that as you melt your way through the ice and it refreezes behind you, two things happen - both to do with the accumulation of "defects".

1) Due to the large volume change on melting and freezing water, a stress field develops around the "borehole". It is unclear what maximum pressure could be developed, but it certainly needs studying

2) More importantly, trace constituents of the ice get concentrated in the meltwater pod surrounding the "boiler", like the "non condensibles" you get when you try to recondense steam that you just biled off, even from clean feed water .(We're NOT talkin temperatures so hot that you do get steam, I was just using a different phase change analogy where human engineers have a LOT of experience in steam engines and power station turbines).

In ice, you're melting everything you meet (except solids and salts, of course). Behind you, relatively clean ice freezes at the highest melting point available for that composition. (If you freeze sea water, you get fresh ice, and saltier water).

Over short tunnels this is not important, but if you're going a long way, then this can become a problem. The chemistry and physics of the whole shebang can get way out of kilter. This issue is known from Metallurgy where a technique called "zone refining" is used to concentrate "incompatible" phases into the end of a metal rod by passing it through an induction furnace and letting a zone of melt travel from one end to the other. You can use this method to either clean impurities out of the rod or to collect them at the end as the "product".

In geology you also see similar processes as large bathes of igneous rock cool and solidify - the "incompatible" phases and elements are concentrated in the last small volume of the rock, which can end up with wierd chemistry - we call these things "ores", sometimes. (There are many other types of mineral/ore deposit too. This is just one mechanism)

In an ice melt situation, the things you would expect to collect as you go along are:-

salts - from windblown sulphate particles, for example

gas - from included bubbles and from clathrates. Did you know that glaciers have clathrate inclusions in them with atmospheric gas as the guest molecules in the host lattice? As snow packs down through firn into coarse ice and then to clean bubble-free blue ice, the trapped air has to go somewhere. Some escapes to the atmosphere, but some is trapped and packed into clathrate molecules

solids - the "water bubble" around the boiler could become quite muddy and gritty

Anyway, I had a good chat with some people who actually listened. The bottom line was that I didn't think enough work had been done on these sort of problems to be sure that a deep probe on the Martian Polar Cap would be successful. In particular, although some thermal ice boring has been done (remember "the lost flight" of P51's that landed on the Greenland ice cap, and one was recovered at great expense?), the bores have never been really deep.

There wasn't really time to do this work before the mission review date, so it didn't get done. In the end, the mission lost out due to the risk of having a giant wind sail to mount the solar panels to get the thermal energy that an RTG would give for free in a simple compact package. Now that RTG's are back on the allowed list, you can expect a future proposal based on this technology, but the zone-refining and stress-accumulation issues will not be sidestepped so easily.

In my view, the next step would be a deep experimental thermal bore in Earth's polar cap with an instrumented package to record pressure (stress) build-up and any odd chemical and phase effects. Watch for a NASA mission to Antarctica sometime...