[Electronic M]

If an adjustable coil can't be adjusted it's bad and must be fixed or replaced.... Especially when it's an adjustment for a stage that's acting up...If a stage is acting up the first thing to do is correctly adjust it, and you only conclude it's a circuit fault when you can't adjust the problem away....Often if you can't achieve an alignment instruction it clues you in to where the fault is.

If one of the adjustable colis on your convergence board was physically damaged and the part of the screen it effects was the only messed up part would you change the coil or troubleshoot the rest of the convergence board?
If the vertical linearity pot was rust ceased and the vertical sweep looked wrong would you fix/change the pot or change every resistor and cap?
If an adjustment that often exists to compensate for tube aging is stuck trying to make the rest of the circuit compensate and do the adjustment is about as much of a rube Goldberg waste of time as you can possibly achieve.