I'm not talking about these supposed stablecoins like Tether, but normal coins.  Let's say an agreement was made among all the major Bitcoin exchanges.  Starting January 1, a Bitcoin is worth $5000 USD, plain and simple, and that's it.  The price never goes higher or lower.  A Bitcoin is $5000 today, tomorrow, next week, next month, etc.  NOTHING changes it.  Not a war, not the economy, not Trump getting re-elected (which he will, he's doing a great job), nothing.

I wonder if that could be done and what the effect would be. 

One effect is that I wouldn't be buying BTC, because with no price volatility, how could I ever make a profit?  But one good thing is that normal companies may be more inclined to use Bitcoin, since its price is now fixed and does not change.