This is not entirely accurate. While MEPs cannot propose laws all by themselves... they can request/vote for the Commision to submit a specific proposal.
The Commission has the legislative initiative. However, under the Treaty of Maastricht enhanced by the Lisbon Treaty, the European Parliament has a right of legislative initiative that allows it to ask the Commission to submit a proposal. [...]
On the basis of a report by one of its committees, under Article 225 TFEU, Parliament, acting by a majority of its Members, may request the Commission to submit any appropriate legislative proposal. Parliament may, at the same time, set a deadline for the submission of such a proposal. The Parliament committee responsible must first ask the Conference of Presidents for authorisation. The Commission may agree or refuse to submit the proposal requested.
A proposal for a Union act on the basis of the right of initiative granted to Parliament under Article 225 of the Treaty on the Functioning of the European Union may also be proposed by an individual Member of the European Parliament. Such a proposal shall be submitted to the President of the Parliament who refers it to the committee responsible for consideration. It may decide to submit it to the plenary (see above).
So while the European Parliament doesn't have the same level of unhindered legislative initiative as a national parliament, it's not completely without one.
The Commision can nay EP's proposals (think of it as a veto), but the EP can also ultimately dismiss the Commission:
The EP can censure the Commission and ultimately dismiss it. So far, none of the eight motions of censure brought before Parliament has been adopted. In 1999, the Santer Commission stepped down before Parliament forced its resignation.
So if the Commission ignores the EP big time (e.g. on numerous/repeated proposals), it's probably not going to end well for that Commission.
And for a bit of background why it is this way:
In 1990, Parliament demanded
for itself a fully fledged
initiative right, not dependent
on the Commission, to address
the alleged democratic deficit
in the then Communities. This
question was discussed again
within the European
Convention. However, under pressure to
confer the same right on the Council, which,
it was feared, might dilute the initiative right
of the Commission and complicate the
legislative procedure, EP negotiators
dropped their demands for a 'direct'
The Council has fairly symmetrical role in this respect
'indirect' initiative right is also conferred
upon the Council (Article 241 TFEU), which
may ask the Commission to undertake prelegislative "studies" of inter alia economic,
social and legal circumstances and to submit
to it any appropriate proposals.
Because of the convoluted procedure, EP hasn't exercised that article 225 right a whole lot:
Parliament adopted 29
legislative initiatives between
1994 and 2009. Since the
beginning of the seventh
mandate in 2009, 18 legislative
initiative reports seeking
proposals from the Commission
have been launched
Up to 2013 when those stats were gathered, the Commission outright refused only one EP proposal.
Besides, how most EU laws are adopted (nowadays) is actually through the so-called informal bargaining...
The IB [informal bargaining] practice leads to the adoption of a legislative act without executing the entire OP [ordinary procedure]. The EUP, the Commission and the Council, indeed, negotiate the legislative measure in ‘informal trialogues’, concluding the law-making process the latest in an early second reading. Introduced in 1999, the use of IB has increased to 80% of the total number of laws enacted between 2008 and 2009, showing its substantial impact on the law-making process overall. In particular, [...] the IB increases the EUP’s effectiveness as a legislator. Through the IB the EUP has the possibility to interact more closely with the Council and the Commission, proposing and discussing amendments more efficiently. IB, therefore, reveals to be more time-saving than the OP. In addition, the EUP may benefit from closer dialogue with other institutions to support its policies.
Actually, more recent stats make the IB responsible for 93% of the EU legislation adopted between 2009-2014.
There's also criticism of IB because it effectively shuts out the small parties. and since the whole IB thing is informal, there's no press/TV scrutiny of how it happens (quite contra to the televised matches in the UK parliament, or even the speeches in the EP). There's some level of public disclosure of the trilogues, but only in about half of them, and even for the rest the information is sometimes incomplete.