I am very much against the thing you describe, whether they call themselves supreme courts or guardian councils or defenders of the constitution. Yes, I am a radical democrat. I think the safeguards supposedly provided by such institutions are largely illusionary.
All sorts of minorities, for instance, may be protected in flowery words, but it isn't worth the paper it's written on unless the majority (of power, sadly, not of individuals) actually care about it. A constitutional safeguard that doesn't have the support of actual power is worked around, it's just a question of lawyer rhetoric. In the end, the only check that can exist on us is ourselves.
That said, at least supreme court judges in the US (and other countries) don't have the power to topple the government, execute ministers, outlaw political parties etc. That's one way the military providing "a check on democracy" is even worse.