The problem with this is that MEPs are elected generally rather than for a specific competency, and then you get stuck choosing between different types of foolishness.
To use an example from the US, the Democrats have generally been the party of Hollywood and proposed a lot of problematic copyright legislation, and a lot of bureaucratic means-tested social assistance programs and loan interest subsidies that do things like inflate housing, medical and education costs. On the other hand, the Republicans have a preposterous position on climate change and the current Republican-controlled FCC is more like Verizon-controlled. So who should I vote for if I want to have a carbon tax but get rid of DMCA 1201?
A solution to this might be something like voters electing representatives on a per-committee basis, but that isn't currently what happens.
You make sure there are opposing parties. Like the house and senate controlled by different parties. It forces them to argue and fight and compromise, but the end results are better.
Compromise is a necessary part of any democratic system, but because it is necessary to represent all of the constituants and balance their needs. It does not mean that it results in better decisions on any particular issue nor does it provide a good way for an individual to get a cross-section of their viewpoints represented fairly.
People treat them as some sort of low stakes national election and they generally penalize the governing party (let's send them a message) and the small parties get a boost. They have no idea which parties/coalitions exist at the European level and where the national party they're voting for fits.
In sum, it's a big joke, to an even larger extent than democratic elections usually are (as argued in books such as Democracy and Political Ignorance or Against Democracy).