Note that BYD doesn't just make BEVs. They're quite big in plug-in hybrids, which aren't in that data. They apparently sold 175k cars in Europe last year. A breakdown of BEV vs PHEV doesn't seem to be available, but 75k of those were one particular PHEV, so it's at most 100k BEVs.
Not saying that BYD is completely irrelevant, but the media overplays them. Presumably because BYD vs Tesla is an interesting narrative, even if the actual figures have both of those as small players in BEVs (at least for cars; BYD _is_ quite big in electric buses), with the real race being between VW AG and Stellantis. VW AG vs Stellantis is a painfully boring narrative.
The EU is a highly protected market, therefore the market share of foreign (to the EU) products cannot be used as a measure for the quality or affordability of such products.
I simply find it noteworthy how fast Chinese EVs are scaling up as a climate change mitigation. I don’t care who builds and sells them, just do so as quickly as possible.
I suspect BYD would do a lot better in Europe if the political class wasn´t afraid of the fallout from the European manufacturers (VW, Stellantis, and all their child brands) being seriously damaged or even wiped out by the competition.
That said, if relations between the EU and the US get much chillier, the EU may decide to make some sacrifices in order to have China in their camp. E.g. VW are arm-twisted into selling Škoda to BYD, with job preservation guarantees, and then BYD is badged Škoda and six months later all the old Škoda models are gone and its EVs all the way.
I suspect that, given people in EU are used to EU car prices, there's not going to be much willingness on the EU side to budge on cars (though the Chinese side may ask for it, of course, and should the EU get them there will be no going back given how much cheaper Chinese cars are).
If things get trade-war-y, American cars are way down the list of things the EU will care about finding substitutes for:
