It doesn't ease the limiting of movement though - it actually restricts the ability of countries within the EU to limit movement, easing the movement itself. If the EU had taken no action to create the EU DCC and the associated regulation, countries would be freer to limit movement than they are now.
The parent comment was correct. The app, in and of itself, is just a tool. Your comment gives this away by including the clause "and the associated regulation".
That being said, it is a tool built for a single purpose. "Papers, please".
If we're lucky, the scope of use for this tool will not expand. I don't like having to get lucky.
It would be great, if the certificate was enough to show at the boarding gate to be able to travel. However, this is not the case – the countries still require to fill long poorly developed forms with a lot of private information. Some of these forms (Latvian forms) doesn't even check the certificate, only asks to check the box that you have one.
It could be worse without the certificate for sure. But I don't think that all this extra effort to set up the system, to deal with falsifications etc. was worth it. The EU could simply make a law requiring to accept the vaccination proof of any country and that would be it.