Now looking at the race-track. Think of the worst case scenario in no wind. Aircraft TAS 60Kt. No matter which way one does it (parallel entry or full racetrack) the aircraft will only be at 6 miles when the inbound turn is commenced. This is an exagerated example of your problem.
I think you mean 2 miles, not 6, right? (edited: Oh no I'm sorry, you mean 6 DME, not 6 from the MK -- yes, quite so.)
But I like the train of thought, because I think it brings out the issue nicely. You're suggesting that, if the descent point is outside the facility used to define the racetrack, it's always possible to choose a speed for which you cannot reach the inbound track before the descent point.
However, there's a minimum speed for initial approaches of 90 knots. Thus I would have thought that, if sector 1 entries to the racetrack are authorised, it should always be possible to fly them at 90 knots, but possibly not at less. And I would have expected a design criterion for the minimum length of the racetrack leg time, dependent on the top of descent for the final approach, to allow that.
For example, if the racetrack leg had to be at least 1 min beyond the top of descent point (which allows something like a 30 degree intercept to work), and that top of descent point were 2 miles from the facility, that would oblige a minimum leg length of (2 miles / 90 kt) + 1 min = 2 min 20 secs. For 120 kt that could be reduced to 2 min, and for 150 kt it comes down to 1 min 48 sec. If you can't protect those lengths, then sector 1 joins should be explicitly forbidden.
But perhaps no such criterion exists.
In the particular case of Calais, it's complicated by some doubt about whether sector 1/2 entries are authorised below 130 kt.