I believe that the stated/claimed intent is to create cross-country, bloc-wide digital signature interoperability and acceptance standards. The theory being that you can "digitally sign" things with a national ID (e.g. a smart card), and have that recognised anywhere in the EU. That would, in theory, help to reduce and simplify bureaucracy, especially for people moving between countries in the EU (a process which can be quite complex even with freedom of movement, due to totally different cultural norms around government systems, forms, languages, etc.)

Something better than typing your name and trusting a third party to do email verification for a digital signature certainly sounds like it could have advantages for doing business though.

I believe the issues identified here seem to stem from a (very) over-enthusiastic desire to have certificate acceptance everywhere (i.e. prevent discriminating against one country's citizens by excluding their ID card CA), without understanding the different types of trust chains and certificate chains. Presumably scattered with a bit of technical naivety as well. The concept itself is (probably?) fine, as long as it doesn't try to force browsers or SSL verifiers to accept or trust certificates they don't want to.