I also fitted a LED tube when the old fat tube supply dried up and I was faced with either a LED tube or replacing the ballast. Fact fluorescent tube rated at 58W and LED rated at 24W it seemed the way forward. However after changing the tube I found the lumen output also dropped from approximately 5500 lumen to 2400 lumen so it was darker than before. Lucky it was bright enough, but on changing I had not realised the drop in output.
I could have replaced the starter only and simply fitted the new LED tube, with the volt drop across the ballast however it would have resulted in the LED lumen per watt being worse than the LED it replaced, so I removed the ballast, however I made a mistake I wired to just on end of the LED tube, which works A1, however if anyone was to replace the tube the wrong way around then it would be a direct short, so the two ends should be wired in series so if it is replaced wrong way around then it would not matter.
It seems there is no standard as to how the LED pins are used, some have one pin either end as line and neutral, but today I am told most have line and neutral one end and other end the pins are connected together giving a short circuit. But having only fitted one myself I can't be 100% sure on that.
It seems the special starter they supply is just a fuse, however the one I took apart did not seem to be simple fuse, however it would seem if the LED starter was put in a standard fluorescent fitting it could blow the heaters.
I am very pleased with the LED tube I fitted, it starts without delay, and is bright enough, but clearly with the drop in light output they are not really much more energy efficient than the fluorescent with HF ballast. The LED lamp is around 100 lumen per watt with the fluorescent at around 95 lumen per watt. This is with tubes, with bulb replacements the LED does shine when compared with the folded fluorescent tube of the compact fluorescent lamp, pun intended. 40 lumen per watt is still considered as energy saving so a CFL at 40 lumen per watt compared with a LED at 80 lumen per watt then the LED is far better than the CFL. But with tubes 100 v 95 lumen per watt then not really worth changing to save energy, but the instant start is really good, and the LED colour is less banded to that of fluorescent (with HF ballast) and very little in the projected life.
Let us know what you think once changed.