There's not much to go on, but here's Ron's initial assessment of the task:
"It's obvious, isn't it?" said Ron. "We've got to play our way across the room."
Behind the white pieces they could see another door.
"How?" said Hermione nervously.
"I think, " said Ron, "we're going to have to be chessmen."
(Emphasis mine.) A possible interpretation of this was that Ron's initial plan was to simply move from one side of the board to the other. Once they got past the white pieces, they could step off the board and get to the door. Since the king can only move one space at a time (and the queen is too important to not use against the white pieces), Ron picks middle-of-the-road pieces to replace, pieces he thinks he can get over to the door.
Later, due to the white team's successes, it seems that the plan changes, and Ron realizes the only way they're going to get through is to take out the king.
There was no alternative.
Keep in mind also that they're racing against the clock, and Ron is an eleven-year-old boy unused to the stresses of facing deadly chessmen in the pursuit of a dark wizard. So maybe he made a lapse of judgement, or didn't think his plan all the way through.
As for why Harry and Hermione didn't object:
"Now, don't be offended or anything, but neither of you are any good at chess--"
"We're not offended" said Harry quickly. "Just tell us what to do."
They trust that Ron knows what he's doing. And at the end of the day, he does get them through the door.