Slightly different but I will sometimes let a slow train go to wait for a faster one, even if the faster one doesn't overtake. I do hate stopping every few minutes!
That's one of my favoured policies, too. In many instances I would rather catch a slightly later train if it is a faster service and hence closes the gap between it and the slower previous train by the time I reach my destination, and the fewer stops the better. I prefer the train I am on to be moving, even if only slowly, compared to being at a complete stop, whether that be due to station calls, signal checks or whatever. At least I know that I am still moving towards my intended goal, even if only gradually!
I frequently use this approach when selecting East Coast services when I travel between York and Newcastle: I inevitably choose the one that flies through Durham, and is around ten minutes faster than the train that precedes it around twenty minutes earlier. It is also no doubt what makes my regular commuting service, the 07:30 Birmingham - Euston "Fast" service, so exceptionally popular, even though it is usually fast in theory only: It's only arrived on time once in at least the last week!
When I have time to spare, I plan journeys I have to take on the Crosscountry network radiating from Birmingham with an eye to which services will be worked by HSTs or Turbostars. I always aim to catch 170s when travelling on the axis between Nottingham, Birmingham and Cheltenham, and 168s between Birmingham, Leamington Spa and Banbury. Or even better, I aim to arrange the times I need to be in Leamington Spa or Banbury for whatever reason to align with the times of the Chiltern loco-hauled services, which I'm usually quite successful in doing. Unfortunately, I am rarely so lucky with the Crosscountry HSTs, as I am generally travelling in the opposite direction for the time of day that they operate
On my regular tube commute from Euston Square, I always hope to catch a train of new S-stock on "the Met", as they offer more room to circulate and the effective air conditioning is a massive boon on the stuffy sub-surface lines. To date I have been largely successful in this endeavour, although I have never yet turned down the opportunity to just jump on the first service that turns up, regardless of what's working it, and I don't think that I will: As rdwarr details, my time is too precious. I'm not at all impressed with what I now know to be C-stock trains on the Circle and H&C lines though.