Don't forget that the servo signals don't run and change at a standard 'tick rates'; only the 20ms frame does. There will then be up to eight servo channels ticked along on approximately 2ms sub-frames, but each of the eight servo pulse can be anything from 0ms to 2.55ms ( 1ms to 2ms in practice ) with 0.01ms resoluton.
A base tick rate suitable for all that would have to be 10us, and with 1us per PICmicro instruction at 4MHz if we did that the PICAXE would be spending almost all its time inside servo handling and execution of the user program would drop to a crawl.
Therefore the ticking has to be far more complicated; on tick expiry determine what to do now and determine how long the next tick will be, set that up, return to main firmware loop.
There's also the problem of main firmware loop and software servo loop being like two entirely independent people, both updating the outputs of the chip; at some point one person ( main firmware, handling High/Low etc ) will want to put something out to the outputs, but between deciding what and doing it, the other ( servo handler ) can change what should be output, and wants to output that. It's a very complicated process to get that to work.
Also for timing critical commands, serial, pulse in or out, counting etc with servo both want absolutely perfect timing but that's impossible, getting perfect timing for one will force non-perfect timing for the other.
Handling all that is what makes servos so difficult. Collisions and collision resolution may only occur once every many millions of internal instructions but that can sometimes be noticeable as jitter.
The only perfect solution would be a multi-core processor and separate ports for digital outputs and servo outputs, a separate servo controller, or taking servo pulse generation and timing into your own hands using PULSIN and PULSOUT etc, but that gets complicated if wanting to control more than one servo channel.
Perhaps the ease of using servos, and how well it works when there are no collisions has led to over-estimations of servo capabilities, expectations of perfection where ( as noted above ) that never can be, with it seemingly perfect at times only by good fortune. One cannot outright say "servo on PICAXE doesn't work" with any fairness because it's entirely satisfactory for many who use it but it does have its limitations. How those limitations will affect things will depend on application, coding and use of servo commands and even hardware chosen.
