Well, if these
> enzymes were really important in digesting food, wouldn't the plant digest
> itself?

Non sense.
breaking done of tissue is regulated in a living organism to maintain the
structure of that organism but as soon death occur an active process of
breaking down start ( that can be suspended by drying ,cooking ,salting or
other means that are used by the food industry ).
.
Ex the detachment of leaves from the branches in a deciduous tree in the
fall is an active process that involved enzymes . Kill a tree before and it
will not loose its leave .
Fruits are also via enzymatic activity reaching perfect ripened stage before
continuing the process toward decay.
Aging of meats involve also enzymes etc...

Nobody yet figured out the difference between a living organism and a dead
one ,same body , one is functionning and the other one not .  denying there
is a difference because of that is simply foolish.

In comparaison with the powerfull enzymes of digestive juices this process
of "natural decay " started by the food itself might not be of absolute
necessity in the avalability of nutrients resulted  but i would not say
either  that it isn't important .
jean-claude