I disagree. This would be quite bad for 4 reasons:
a) We already have Restoration keyword, which essentially does the same, under some conditions.
b) Legend keyword is supposed to be powerful as its name states, the cards represent unique characters or creatures.
c) It's already harder to get a rare in your hand, since summoning cards that don't specify summoning a rare, won't do it anymore, so the Legend keyword is not so usual as it was before
d) A random +1 facility is not that overpowered effect, given the fact that it's random, and it's only +1. The randomization deduces from the power of the keyword enough already, so no further twitching is needed. Also increasing only 1 of your facilities is relative easy. You can use commons at 14 resources with conditions, or uncommons at 10-12 resources. Here you use a Legend usually at 30-40 resources. Since when we use legends we need this massive amount of resources, a random +1 facility is enough to compensate for this. Making it increase your lower facility means you have to play 3 legends before you can increase again the desired facility. The randomization might or might not increase your facility, and that's why it's a far better negative feedback than a controlled +1 facility condition, considering the damage power of legend cards
Sorry for bragging this long.