grundsow,
Deer will eat beechnuts, but not as a high-priority food. In addition, beechnuts are so small that it would take a huge number of beechnuts to feed deer--far more than the trees can produce. Beechnuts are valuable for other wildlife though, especially turkey. I've seen killed turkeys with crops full of beechnuts.
From a deer "food budget" viewpoint, I don't even consider acorns. They are a very high-value food source in fall, but acorn production can be very "iffy." I do all my winter food budget calculations using only natural browse, and consider acorn production just a "super bonus" food source when they exist.
As you mentioned diversity in habitat is the key, and I do want
some of a property in long-visual-range, open-understory mature hardwoods. Visual ranges in these big oak stands can be amazing--well over a 100 yards in the most mature stands. Now I certainly don't want
all or a majority of a hardwood property in this habitat, but having some is a good idea.
I want
some of a property to look like this. But also notice in this picture the trees with the tan leaves. Those are all young beeches, and this is probably the lowest density of beeches I have anywhere on my property. In many locations, they completely dominate the understory:
Unfortunately, anywhere where sunlight can get under the canopy, especially where timber has been thinned or removed on a hillside, the sun can get under the canopy of the timber on the ridge-top, and beeches rapidly dominate, greatly reducing visibility. One of the habitat tactics I like to use is to create thick bedding cover along steep hillsides, but to leave the mature oaks standing on the ridge-tops. This can draw deer up from their hillside beeding areas to feed on acorns along the ridge-tops, increasing harvestability. But the beech growth eventually chokes out all visibility on those ridge-tops bordered by hillside timber cuttings.
But again, whether or not to recommend someone plant beeches who has NO beeches is very different than
promoting beech in a hardwood environment. They absolutely
can become a problem over time. Their shade tolerance eventually allows them to serious interfer with oak regeneration in hardwood thinnings and can cut hunting visibility to very short ranges.