As an untechie, I agree with a lot of what you're saying, but still find it hard to understand why if the boiler's off for five mins and then on for, dunno, eight minutes, it's less efficient than it being on for a solid 13 minutes.
If we assume that our desired output during those 13 minutes is constant - 20kW for arguments sake, in a steady-state condition our boiler could provide a nice smooth 20kW for the duration such that the input matched the output and, by definition, efficiency is achieved.
If, however, the boiler is going to be off for 5 minutes and on for 8 then the latter part of the cycle will need to compensate for the 5 minutes at 0kW by burning at 32.5kW for the 8 minutes (from (20x13)/8). In this hypothetical scenario this 32.5kW might be outside of its capabilities, or if a condensing boiler then its ability to condense, and we have increased our likelihood of overshoot. All of these are inefficiencies compared with the steady-state non-cycling operation. Furthermore, this is just one cycle - it's the repeated cycling inefficiencies that eventually add up to a potentially significant waste of energy, particularly given some of the problems with ignition I mentioned earlier.
Say you're in summer now - same boiler etc, but you're only heating the water circuit. That'd shut off pretty quick, surely. What do you do about that, apart from knocking the temp back a bit?
There's not that much you can do, other than relying on the cylinder stat to indicate it is satisfied prior to the boiler running itself continuously. If the cylinder stat is set to 65C and the boiler is set to 55C then, yes, it'll have no option but to continuously cycle. Going back to matching input to output if the cylinder cannot extract the heat at a rate that the boiler is producing then we'll get cycling - we've simply created the ultimate mismatch in this scenario.
If you cruised down a hill in neutral in a car, you'd use less fuel than driving down or on overrun!
Be careful with analogies as they all too often don't compare like with like, particularly when the important bits are the nuances which get conveniently left out! In this case I'd disagree anyway with your premise. You'd use less fuel on overrun because the injectors would be turned off for the duration hence zero fuel usage. When in neutral your engine would have to at least idle, to avoid stalling, hence you'd still be burning fuel to keep it ticking over.
Not trying to be flippant, but there must be a balance when time off v time on. No idea what it is, mind. But there must be one!
If you were to graph a chart of instantaneous energy consumption vs time for a boiler that cycles on/off/on/off/... and compared it with a continuously running modulating boiler you would see that the former would be stepped, perhaps saw-toothed, whereas the latter would be smooth. Going back to our definition of ultimate efficiency being where input equals output the smooth curve would necessarily win every time given the inherent inefficiencies of stopping and starting.
Edit to say: I'm making the times up but they're not far off what I get with my (oil) burner. ** When I say 'efficient' I mean uses less fuel.
Moving from the theory to practice others might be able to comment on what is acceptable for an oil burner, and what measures you can take to increase its efficiency.
Mathew