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A friend of mine and I are giving this idea some thought too. In some simple receivers a varactor (or common one too) diode is used to shift the oscillator frequency with a dc voltage. I know in some remote tuning applications a varactor is used in parallel with other capacitors to provide some adjustment to a loop antenna. I don't think the range is that broad but it's apparently a useful alternative to other methods. Implementing this in multiple circuits in multi-stage receivers might be tough.
Take a look at TDA1072. This is a superhet receiver chip, and on p.18 they show a schematic which has electronic tuning. Getting the local oscillator to track the antenna tuning seems like an alignment nightmare, but I'm no expert on radio receivers.
I believe this chip is designed so that it could be used without tracking RF tuning. It would require very steep skirts on the IF filter. If there are any hams reading this, they may know whether this is true or not.