Yes, that might make some sense (though there's now the TfW service if you want to do Liverpool-Chester quicker) but Merseyrail demonstrates the benefits of a consistent, simple, all day Takt (you basically have to remember one number and be able to add multiples of 15 to it and it gives you the entire timetable including connections, pretty much) and I would not be in support of anything that weakened that.
The one thing I'd
possibly concede to would be a few semifast peak extras as the Swiss do (the land of the Takt
) but I would only support these if they could be wholly overlaid, i.e. they didn't require any adjustment whatsoever to the base Takt, not even a minute here or there. This might work by sending them out 1 minute in front of the "base" service. But then if you're going to do that (which means you've got a spare unit to do it) you might as well just couple them together and run a 6/8 car service instead.