The main disadvantage of bolt action is that one has to remove the right hand from the trigger which leads to slower rate of fire. Neither lever nor pump have this problem. Rate of fire was viewed as an important military issue which lead to development of repeating rifles in the first place. Nevertheless, all major WW1 rifles (Mauser, Lee-Enfield, Mosin-Nagant, Springfield, tube(!) magazine Lebel) were bolt action. WHY?
The lever action mechanism does look "flimsy" (not "military-grade strong") when opened, this, I guess, might be the reason not to use it (although the Russians used Winchester Model 1895 - but they were generally starved for weapons).
When firing from a trench (with the rifle lying on the breastwork), the advantage of pump action obviously disappears (and could even be a liability due to dirt getting under the slider) - but no army planned to fight from trenches before the WW1.
The bolt action rifles were using more powerful center-fire cartridges (in box magazines) than the rim-fire cartridges (in tubular magazines) usually used with lever- and pump-action guns. This does not sound like a good reason - I don't see why the slider in pump action gun cannot operate the same magazine as the bolt-action.
So, how come all the major WW1 rifles were bolt action?
Why didn't they try to make a pump action rifle with a powerful long-range cartridge? (it's not impossible, e.g., Remington Model 7600)