Marc Elias has a theory:

One possibility is simply bad legal strategy. Republicans and their attorneys regularly make litigation decisions that defy common sense and at least some of the attorneys in this case have a history of bringing meritless voting cases.

More likely, however, is that the GOP plaintiffs and their attorneys want to lay a predicate now to contest the 2024 election. Just as former President Donald Trump and his allies did after the 2020 election, Republicans are planning on blaming the voting rules for why they lost. They will couple it with an attack on the courts and false claims of fraud.

I suspect that their plan is for this case to remain pending and unresolved by Election Day 2024. That would allow them to use it as a cynical tool to claim election fraud and illegal voting rules robbed them of a fair outcome. It would give them a basis to contest the outcome of the Michigan results once again in court and Congress. When they fail, it will fuel their pathological election denialism.