I have five trees I am wanting to remove from my inground collection as they are late and just don't do well with production in my zone. Space is an issue so I am wanting to plant new trees in the same spots. Would this cause a problem?

As long as the previous figs were healthy and grew well, there shouldn't be a problem. Just watch fertility as the soil may be a little depleted. As the old roots rot they soil microbes may suck up some of the available nitrogen as well, try your best to get most of the roots out.

As long as there are no signs of nematodes on the old roots should be ok

Hi,
To avoid the old trees coming back with shootings, I would well crush the area and remove all the roots from the previous trees.
I would try to plant trees with differences that are easy to spot - just in case a sucker comes from the ground, it would be easier to be sure that it is
the new strain and not the strain from the old tree.
Fertilize more the area as a previous tree was at that place before.
If the old tree had FMV or nematods... surely not a good idea.
What you could then do, is dig a hole and put an 80Liters bottomless dark plastic trashcan, and fill it with new compost to avoid spreading the diseases between the old and new trees.
I'm trialing that king of setup ... To avoid rodent damages ...

I make an occasional pleached tree which is just putting 2 or more trees in the same pot and braiding them so they will eventually grow together. This obviously requires putting more then one tree in a pot (or hole) and does not create problems.