Die Karte von openstreetmap.de zeigt Dir deutsche Namen an, siehe https://www.openstreetmap.de/karte/

Einige Kartenlayer, die auf www.openstreetmap.org auswählbar sind, bieten englische Beschriftungen weltweit, z.B. osm.org/#map=6/29.40/108.06&layers=T oder osm.org/#map=6/32.53/50.30&layers=C

Weitere Varianten (auch mit anderen Sprachen), gibt es von osMap, siehe osm.wiki/OsMap , z.B. auf Englisch: https://www.osmap.uk/#9/35.6740/139.6335 oder deutsch: https://www.osmap.de/#13/37.9581/23.7423

(c) OpenStreetMap contributors for a wonderful basemap, even though this one is non-retina.

~OSM-Carto: Perfect pizza basemap, not cluttered or overloaded with information at all.~

Actually the osm-carto style is one of most sophisticated map styles out there. So I would not define the “Standard” layer a bad solution, esp. since it is wildly recognized, known and an OpenStreetMap household name. (It is only not a suitable basemap if you add a lot of data on top as the style has lots of useful OSM data based information baked into the map style already).

It is just a bad idea - as rightly stated by you - to use the tiles from tile.openstreetmap.org instead of either self-rendered, data-monitored tiles or one of the third party solutions out there.

But yes, I’m probably biased as someone who provides tiles as well (where some of those tiles produced closely resemble the osm-carto style, just with extras like different language labels or retina support).