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No. Very bad idea.
Normal mode is the base game experience for the newcomers. For us veterans who played Terraria for a long period of time, we got used to its mechanics and quirks, but, when Expert Mode first came out, I'm sure we all faced a lot of trouble trying to get used to the new damage values and difficulty curve.
Now, picture yourself as a first time player who doesn't even know the basics of the game, directly getting thrown into an expert world. That's akin to playing Dark Souls or Cuphead, having to die way too many times in short periods will just push you away from the game and prevent you from further discovery and getting used to it.
Normal mode is indispensable and should never be removed because it allows new players their sweet time to get used to the game and learn about it before moving to harder difficulties, and, in addition to that, it permits veteran players to try challenges or runs without worrying about getting slugged by slimes and the likes.
On the steam achievements page for Terraria, 52.1% of people have killed at least one boss (Eye of Cthulhu) while only about half (23.5%) have killed the Moon Lord. I assume that people who play on Expert have at least beat the Moon Lord once, so this would show that most people who get into the game can't or won't beat Normal mode.
I would never personally support removing Normal mode, as I never am in favor of removing original Terraria content when there is any other alternative.
Sometimes bugs fixes/optimizations require dramatic fixes to prevent certain issues, but that should always be last-choice scenario.
Simply removing an entire mode for no other reason than "it doesn't serve a purpose" seems like a poor decision to me.
Also, to echo some sentiments here, Expert is NOT the "standard mode for play". The greater majority of players never frequent the forums or Discord, and many of them play on Normal and we never hear of it. Mathbrush's point about the achievements is telling: we dramatically over-estimate how far many people get into the game, because our immediate circle of reference (forums, Discord, etc) has a non-representative sample of more dedicated players.