| All is around a compromise what the lamps are optimized for, whether more emphasis is on the wider range ballast compatibility, or highest efficacy. As everywhere with any engineering, you can never have all. So the F13T5 design is optimized for something else than the F14T5. To big part it is given by the era when their development happened and what technology was available at that time.
First it is not rue the "electronic" induces worse wear than "magnetic", even on starting, PROVIDED ballasts with the same starting sequence are compared, so how the ballast treats electrodes before, at and after ignition and then during operation. If all is the same (e.g. cold starting), the low frequency "magnetic" will lead to faster wear.
Now "the devil in the detail" is in the fact that the simplest European "magnetic" ballast is a glowbottle preheat, which, as the name sggest, (at least partially) preheats the electrodes before applying high voltage for ignition, so the ignition happens on electrodes with at least some emission, so partially reducing the starting sputter wear. It is by far not perfect, but it does reduce the sputter somehow. On the other hands the cheepeese electronic do not preheat the electrodes at all, they essentially apply the high voltage so ignite the discharge immediately and warm up the electrodes later (partially by the high dissipation from the high cathode fall, partially by supplying elevated heating current through the filament). So the discharge operates few 100's ms on cold filaments, so with heavy sputtering. So the reason the cheepeese electronic ballasts do wear the lamps faster on starts is not the HF electronic to be inherently more damaging, but because those ballast designs are cheapened so much.
A decent ballast first warms up the electrodes (for about a second or so) and only when their temperature is sufficient for thermionic emission, they apply the high voltage burst and ignite the lamp. This way the starting wear could be practically completely eliminated, if the parameters are correct (preheat voltages/currents/time; usually ballasts with longer times, like 2s or so, tend to wear the least), but the consequence is a 1 or 2 second "delayed" start, which is "frowned on" by uneducated users, so becoming a marketing problem. Therefore most decent ballasts are somewhere in the middle, where the starting wear, as well as starting time are somewhat a reasonable compromise.
And it is not "single electrode only", it is really both electrodes stressed the same way. The electronic are even way more symmetrical drive on the lamp than the magnetic, by the way, because their circuit features a series capacitor blocking any DC currents.
The "magnetic" ballast feeds the tube with a rather low frequency sinewave feed means the cathode spot (the arc root) is heated by the cathode fall only one half wave (10ms), then another halfwave is effectively cooling down and then it has to support the reignition. For the reignition to be least damaging (it is essentially the same ignition as lamp start, there are just more free charge particles remaining from the previous half cycle), you need the spot that becomes the arc root hotter than the minimum thermionic emission threshold. On the other hand after it is fully loaded by the arc current the 10ms, its temperature reaches its peak and it should not rise too much, otherwise the emission layer would boil off too quickly. So you need these two temperatures to be as close as possible.
Because the 20ms cycle is quite long time (for the thin layer), the only way maintaining both reignition (the minimum) and the peak temperatures close to each other is to provide heavy filament underneath and a rather thin emission layer. That means if the lamp has to work sufficient lifetime with such supply, the electrode filament needs to be quite large in surface, so lose quite a lot of heat, which should be replenished during operation to maintain the minimum operating temperature. And this consumes quite some power, which then can not generate the light.
But if you are designing a lamp for an electronic ballast only, the high operating frequency (so the warmup/cool down/reignition cycle is very fast, taking 30us or so, so about 600x faster than the mains frequency) means even the tiny arc root spot can not change its temperature that much so does not need any of the aids smoothening the temperature variations, so big part of the electrode losses could be eliminated. The consequence is, if someone operates that lamp on 50Hz, the arc root temperature variation over the supply period (20ms instead of 30us) becomes way greater, with the peak temperature too high (so the emission layer boils off) and the reignition too low (so the reignition happens with essentially a cold cathode, with the related sputtering).
The F13T5 were designed in the 40's, when anything else than the mains frequency was just not available, so the F13T5 has electrodes designed to coop with the low frequency, on the expense of the extra losses there.
The F14T5 were designed at the time when the HF electronic ballasts were already somewhat established norm, with the highest possible efficacy as the primary goal, even when that means it could be used only with the HF electronic ballasts.
In fact the F14T5 being slightly longer than F13T5 is not because the extra length would bring anything (they both are aimed at the same fixture format/size and that small difference does not bring anything in the efficacy), but intentionally to prevent them being installed in the F13T5 (magnetic ballasted) fixtures.
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