The difference between ASN.1 (BER/DER) and modern binary encodings is that people have tried to parse the former by hand but not the latter (at least to my experience). BER/DER itself is a fine encoding---sure, it has a legacy including six string types but we can deal with them---and in principle a simple library with bound checks should have been more than enough.

ASN.1 is however structured in a way that such a simple library looks like incomplete; it looks like that a correct way to parse BER/DER is an ASN.1 compiler, which tends to be bulky and annoying to integrate. As a result for a long time most ASN.1 implementations were either a "complete" ASN.1 compiler or a hand-crafted parser, with no middle ground of a library that is simple enough and prevents you from memory unsafety.