This one's occurred to me and would very much be my preference, too. Other federal courts use a similar system, so it's not like we don't already do this.
> It also means the Supreme Court considers every case before it. The current system of throwing out cases because they’re hard or boring is so silly.
Some Supreme Courts only decide on constitutional issues, or if someone believes a constitutional right has been denied. It depends on the country. Some countries' Supreme Courts also examine all cases submitted, but, if the Brazilian example serves, it can take many years for a case to be seen. Pushing up criminal cases is a common strategy to exhaust the time window in which a case can be prosecuted.
> Some Supreme Courts only decide on constitutional issues
These are usually referred to as constitutional courts. Because the Constitution vests "the judicial Power of the United States" in "one supreme Court," ours is also the court of final appeal.