The obvious reason is that finite groups are easy to compute with, and infinite groups are not - the fact that the decision problems mentioned are solvable for (some) hyperbolic group is of essentially NO practical interest. For practical purposes, you need residual finiteness, and of the effective kind (see the oeuvre of Khaled Bou-Rabee and yours truly for examples).

The obvious reason is that finite groups are easy to compute with, and infinite groups are not - the fact that the decision problems mentioned are solvable for (some) hyperbolic group is of essentially NO practical interest. For practical purposes, you need residual finiteness, and of the effective kind (see the oeuvre of Khalid Bou-Rabee and yours truly for examples).

The obvious reason is that finite groups are easy to compute with, and infinite groups are not - the fact that the decision problems mentioned are solvable for (some) hyperbolic group is of essentially NO practical interest. For practical purposes, you need residual finiteness, and of the effective kind (see the oevre of Khaled Bou-Rabee and yours truly for examples).

The obvious reason is that finite groups are easy to compute with, and infinite groups are not - the fact that the decision problems mentioned are solvable for (some) hyperbolic group is of essentially NO practical interest. For practical purposes, you need residual finiteness, and of the effective kind (see the oeuvre of Khaled Bou-Rabee and yours truly for examples).