Java, before version 8, couldn't handle DH parameters larger than 1024 bits, so that may be a motive. But I suspect a large part of it has to do with the fact

Java, before version 8, couldn't handle DH parameters larger than 1024 bits, so that may be a motive. But I suspect a large part of it has to do with the fact that OpenSSL left DH parameter configuration (also ECDH curve selection) up to application developers, who don't really have the qualifications to make an intelligent choice. As a result, some applications make the administrator provide their own DH parameters file (and if you don't, no DH for you), others just hard code parameters (usually 1024 bits long, or 512 bits if the export flag is set) into their source code, and others dynamically generate them (and may or may not let you specify the length to generate). Unfortunately, this means that it's not a question of what OpenSSL can do to mitigate this, but what every single server application using OpenSSL has to do.