With the technology the Federation possesses, voting should be a near instantaneous process.
Not necessarily. Back on TOS, the Enterprise
was constantly visiting remote colonies and settlements that had been out of touch with the Federation for months.or even years. And even the Enterprise
wasn't always able to communicate with Starfleet Command instantaneously. Technology had its limits.
Space is big.
Yeah, tabulating the vote on Earth is probably pretty streamlined, but getting the polling results from Deep Space Station K-7 or the Icarus Colony way out on Gamma Sigma VI . . . .
(Especially when the tribbles keep getting into the voting machines!)