I don't think you understand how legislatures around the world work, if you think this wouldn't be gamed to absurdity.
Important bills generally don't go to a vote unless everyone involved knows exactly how many votes they are going to get. Your proposal won't actually stop anything that a majority wants passed from passing - as long as a minority can't get ahead of them by poisoning the bill.
Bills are not single-issue. Any bill - even the best - can be trivially tanked by attaching a bunch of awful garbage to it. You are giving a single person (or whatever the minimum quorum is for putting a bill to vote) the power to kill, for years, progress on any issue - by putting forward their own version that's saddled with crap.
This would immediately be abused to disastrous effect.
You will end up with a complete farce, with the minority trying to outdo itself by coming up with the worst possible bills imaginable, that happen to include slivers of a majority's agenda. It's completely ass-backwards way to approach any decisionmaking process - because you are effectively giving multi-year issue veto power to any member of a legislature that's willing to embarass themselves by proposing garbage (that they don't actually want passed).
Or, worse yet, the majority will take the bait, and pass the bad bill anyway (because if they don't vote for it now, they won't get the chance to revisit the issue for years).