I more or less agree with you on this. How do you handle such a player, though? These days, instead of outright rejection I’ll just say “Amazing! Seeing as this is set in a pretty cold environment, how can we tweak your awesome character so they don’t immediately die of exposure in that chainmail onesie?”
I’ve seldom met a player who isn’t open to compromise if approached positively. I suspect your experience is similar.
If someone is gaming at my table, either I or another member has already vetted that person and is confident they're a good fit for the group, who is not going to be intentionally disruptive or disrespectful. It's not a particularly high bar, and we've had no issues maintaining it. I can't imagine a player ignoring everything we've discussed about the nature of the game, failing to engage in any kind of constructive feedback and settling on a concept without reference to the sort of game we're actually intending to play. The whole situation feels nonsensical to me.
If a player
did come to me with some option that seemed, at face value, to be completely inappropriate, I would expect that they had already considered this and had a work around in mind. If I concurred and we could reach an agreement about how it would work, then sure, we'd go ahead. If not, I'd say no, and they'd go with a different idea. In the latter case, I'd also be mindful of all this and look for ways I can help facilitate what the player was looking for in future games (I might even have an idea in mind already: "Hey, you know that I want to run such and such at some point, this concept would probably work well in that setting/system/whatever.")
Beyond that, I can't really comment on a player randomly proposing a lizard man in an arctic game without a huge amount of additional context. What are the actual themes and settings of the game? What ruleset? Why do they want a lizard man in this specific game? We use calculating gsheet character sheets, how easy will it be to modify these sheets to allow for this character in this game? (On this one, I've started making an effort to make sheets that are easier to modify to include unexpected features, even if it results in a little less automation up front.) What other impacts will this have on play?
In reality, players proposing strange things in my group are invariably doing so at the edges of, and not far beyond, the type of game we've agreed upon. When I've run truly wide open games (using HERO or Ascendant), I will have players say "Can I do X?" just because they're not sure if the system can handle it, and my response is always going to be either, "Yes, I'll show you how," or "I assume so, let's work out how." In a game with more limits on the starting condition, questions are always ones made in good faith. "I'd like to work this into this concept, is it feasible?" and, if we can find a way to do it, of course we will. I've also found it's the case that the players with the most out there concepts tend to have half a dozen interesting concepts, so they're not arriving with this single, fully-formed idea that must make it to the table in this game right now, they're testing the waters, trying to whittle down their list of options to just one, so a tentatively negative response is likely to be helpful to them, rather than a road block.