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It's meaningless in the sense that it doesn't have a meaning that matches what you're trying to use it for. Not that it literally has no meaning.
It depends on what you're trying to measure.
If you're trying to measure what percentage of experiments have heads, you need to use a per-experiment probability. It isn't obviously implausible that someone might want to measure what percentage of experiments have heads.
What I'm trying to use it for is to compute P(Heads), from a halfer position, while carrying out my argument.
So in other words, P(per-experiment-heads | it-is-currently-Monday) is meaningless? And a halfer, who interpreted P(heads) to mean P(per-experiment-heads), would say that P(heads | it-is-currently-Monday) is meaningless?