I would think the Romanian and Moldovan populations would want this, regardless of the EU. Smaller states aren't always better, especially considering Moldova is one of the poorest countries on the continent. The Moldovans would benefit from being a European Union member, having more opportunities for work, travel, and education, and also being a member of NATO, giving them protection from Russia in case Ukraine doesn't hold them back. Romania would see it as a reunification with what is their historical lands. There are more benefits for the Moldovans than Romanians IMO, but both still seem to want it. The EU would have to invest heavily in both, yes, but the strategy of investing heavily into struggling members paid off many times, a good example being Poland, being incredibly poor when they joined, to now a European powerhouse after getting the money they needed. I believe when Romania and Moldova unify, the EU would be willing to invest, especially in their defense and infrastructure.
Also just wanna say that Russia Today (RT), the network responsible for the article OP linked, is a particularly shitty news network, and of course they would focus on the negatives of the reunification. Every inch of land that goes to the EU and NATO is a humiliation to them, and they will try everything to make sure that the general population is against it. Another article in relation to Moldova realigning with the European Union : "This European country is preparing to give up its future for an ‘EU dream’" is clearly just Russian propaganda. Please OP never use this bullshit as a source again.