Carbon Capture, page-317

It's an interesting article and it shows that there is a lot of work happening in Europe to further develop e methanol production.
There is an interesting article about thysenkrupp working on this process:
Thysenkrupp e methanol

Another article with some of the big European companies involved in the e methanol projects:
Freighwaves

So yes, conversion of CO2 into e methanol or green methanol is a feasible, proven technology with many big players involved.
Yes there is always room for improvement and there will be progress which will get the technology better.

The problem as usual is in details or in this case costs.
Methanol produced from fossil fuels has production costs in the 150-250$ pet ton range.
E methanol produced using renewable energy costs 800-1,600$ per ton with the cost of producing green hydrogen being the largest part.
Very good article on potential and obstacles here:
Clean energy news