This is part of a long-term effort to foster some European-wide debate and make this election about European issues, as opposed to purely national ones and generally make the EU more democratic and strive for something like a parliamentary regime, with a “cabinet” (the Commission) supported by a majority in parliament. Importantly, the Parliament is the one EU institution whose members are not named in some way by national governments (commissioners, EUCJ judges, members of the court of auditors, etc. are all named by each country's government).
The intent is apparent in all the changes to the election of the parliament and the nomination of the commission over the years. The European Coal and Steel Community already had a parliament from its creation in 1952 but the European Parliament is only elected directly since 1979. Then, in 1994-1995, the term of the third Delors Commission was shortened to align the next term with the European Parliament's term. And in 2014, European political parties also put forward “candidates” for the presidency of the Commission who debated on TV, much like parties in parliamentary democracies name a leader before an election.
It's only loosely related to the election itself but it's interesting to note that until recently, MEP would receive salaries identical to that of MP in their country of election. It's only since 2009 that they all receive the same pay, another step in disconnecting the European Parliament from national rules and concerns. All this has been a mixed success at best but de-syncing elections to the European Parliament would run contrary to this long-term trend.
Finally, note that doing so would create some practical problems for countries that never organise several elections concurrently (I am thinking about France for example) and potentially many many elections in short succession, although it's not too difficult to imagine some pragmatic fixes for these issues or to simply let countries do as they see fit.