It would be hard to exaggerate just how much the US model of supreme court has been rejected by the modern democracies of the world. On three dimensions, the US model is really rare: appointment procedure, tenure, and size. And, yes, we should be actively pursuing reform in all these dimensions.
I am going to reference the data in A Different Democracy, which covers 31 countries.
Countries that allow a popularly elected president to nominate, contingent on consent of a malapportioned second legislative chamber, with no extraordinary majority needed:
2 (Brazil, US)
(Two others are by president and 2/3 of senate: Argentina and Mexico)
Countries that provide life tenure to supreme court judges:
3 (Argentina, Denmark, US)
Countries with top court having fewer than 12 members:
7 (Argentina, Australia, Brazil, Canada, Mexico, New Zealand, US)
Countries with all these characteristics: 1
In general, other countries either require extraordinary legislative majorities (such as cases mentioned above) or involvement by non-partisan commissions. Many have terms of several years (usually longer than those of the elected bodies), although quite a few have retirement ages (usually 70 to 75, sometimes younger).
Parliamentary systems often have appointment by the cabinet, and while that sounds quite partisan, I am not aware of other countries that have such politicized appointments as the US has nowadays. There may be some clear reasons why formal executive discretion over supreme-court appointment is not a source of controversy in established parliamentary democracies (to my knowledge), but I can’t claim to know what those reasons are.
It is noteworthy that presidential systems have mostly moved away from anything looking like the US model, and for good reason. The processes that most resemble the US would be those of Argentina or Brazil, not normally countries Americans want to consider peers in terms of democratic process, but actually comparisons that are quite apt.
(Also: not considered here, but covered in the book, is that several countries have constitutional review in a separate tribunal rather than in the apex court. Most such countries are civil law jurisdictions.)