[iacelmiv]

Points are not American, they are used for typography in Europe and everywhere else equally as much as in the US.

The metric system is poorly suited for font sizes. Most designs require a series of sizes within a small range: a typical book or poster might use 9pt for footnotes, 12pt for main text, 16pt for subtitles, and 24pt for titles.

Aesthetically speaking the most attractive ratios of sizes are small ratios like 3:2 and 4:3. Using points it is very easy to construct an attractive range of font sizes like my example above. It is difficult to imagine how this would look in a metric system that's not a mess.

[perilunar]

Font sizes would be perfectly fine in millimetres. 9 pt ≅ 3 mm, 12 pt ≅ 4 mm, 18 pt ≅ 6 mm, 24 pt ≅ 8 mm. The difference is about 6%.

[WillAdams]

A 6% difference in type size would markedly change number of characters per line, number of lines per page, and pagination.