Last year the Rabbanut made the same suggestion, but as far as I could tell it was largely ignored, possibly partially because the decision was announced too late and people had already made plans. This year it seems that more people are making Medorot on Sunday afternoon / night, at least in Modi'in - all my kids had bonfires on Sunday, not Motzei Shabbat.
Not surprisingly, segments in the Haredi community have rejected this suggestion - claiming that they will not be Mechalel Shabbat, and if other people have to be Mechalel Shabbat to provide security and safety requirements in Meron, that is not their problem.
Rabbi Slifkin at Rationalist Judaism has an excellent post where he discusses this problem.
An anonymous commentator on Life in Israel ridiculed the whole idea - asking how Medorot on Motzei Shabbat would prevent people from keeping Shabbat who otherwise would have:
I'm curios who the Shabbos desecration is coming from? Religious people who know not to drive on Shabbos? Irreligious peeople who would otherwise keep the Shabbos the day before Lag B'Omer? Are there any studies that show that people who used to be Shabbos observers decide to abandon their beliefs to attend a bonfire?
Well - today Radio Kol Chai is reporting that a religious firefighter has been ordered by his superiors to travel to Meron on Shabbat - you can read the story here: http://www.93fm.co.il/radio/111333/
I have no idea how the issue will be resolved for this firefighter - will he get a heter to travel on Shabbat? Will he spend Shabbat in Meron away from his family? Will he simply defy the order, and if so will this cost him his job?
None of these options sound good - and whatever action this firefighter takes, I'm sure that there are many other firefighters who are religious or traditional and do not normally travel on Shabbat, but will be pressured to this year.
So the short answer is that there are large forces within the religious community that believe that the relatively new minhag of bonfires on Lag B'Omer is more important than Shabbat. Curious to know if these people who aren't bothered by other people being Mechalel Shabbat on their behalf are equally happy for businesses, buses, or car parks to operate on Shabbat - or do they only think that Jews should break Shabbat if it is for the benefit of the religious community.
By the way my brother has 2 interesting blog posts about the histor (or lack of history) of Lag B'Omer here and here.