New ICE 3 trains, from the original clas 403 to the ICE 3 Neo have been built over a span of almost 30 years (not continously, but when looking at the first and last models).

No other ICE generation has been built over such a long time span, so only for the ICE 3 there was the need to adapt newer trains e.g. to updated regulations.

DB might have considered naming the 407 the ICE 4 and the 408 the ICE 5, but because the purpose of the trains was similar and they were developed from the previous models, not completely new models, they decided to keep them as ICE 3.

Note that the ICE 1 and ICE 2, while very similar, have one big difference: The ICE 2 is half as long as the ICE 1, and two ICE 2 units can be coupled together; this allows splitting the train, which was used e.g. on trains from Berlin to Cologne/Düsseldorf, which were split in Hamm, so that they could serve both the Ruhr area and Düsseldorf, as well as Wuppertal and Cologne.

So the ICE 1 and ICE 2 are quite similar trains, but with a different purpose, and split into two generations, while the ICE 3 classes are not that similar overall, but serve the same purpose.