I really don't get why people focus so much on the court becoming more conservative.
Hasn't the court (with the exception of the Warren court) always been more conservative?
It usually matches the country's alignment. It takes a few years to catch up after every alignment. The last two alignments saw matching Courts and part of the Lincoln - McKinley one too (I can't be arsed to see when the Courts became Lincoln GOP but I know by the 1920s they were extremely conservative and Republican).
The Roosevelt Court went from roughly 1937-1986 and the Reagan court was probably after Rehnquist become Chief Justice. Maybe when Thomas joined the Court replacing Marshall in 1991.
Reagan appointed 3 justices, Bush 2 (one turned out to be liberal) but combined with Rehnquist the Court became decidedly conservative by 1991 at the latest. Every Court appointment between 1969 and 1993 were GOP made. But a lot of Nixon people were moderate to liberal. So was Ford's lone appointee.
The federal judiciary has been more conservative than liberal on balance since the 80s in their rulings.