Is it good for the airlines and airport? Yes. It reduces the cost at check-in, and (as has already been said) potentially increases the spend once you're through security. Security itself may be slightly more expensive to run, but there's probably not much in it - all passengers go through security and most have a bag of some sort anyway (whether it's a suitcase or a handbag).
Good for passengers... not necessarily. Some people do benefit - fares can be cheaper without luggage*, and it is usually quicker at both ends if you don't have a hold luggage (although of course the passengers who would benefit need not carry hold luggage in the first place). Reducing the size of cabin baggage, even with complimentary hold luggage, will disadvantage many who prefer not to check their baggage in (which is probably disproportionately the higher-yield business passengers). As I've alluded to, if hold luggage grew at the same rate as passengers I think that airports would not cope today and would require additional baggage handling systems and staff - which would ultimately manifest as higher fares for passengers.
* It is likely that some airlines use hold luggage charges purely as ancillary revenue, but it is reasonable to say that lots of airlines also charge lower fares because they're not carrying luggage. There's no way that the lowest fares would exist inclusive of luggage.
Do you have figures to back this up? I ask because thinking about myself (I might or might not be typical, but I do fly a lot), I am more likely to be forced to check bags in on budget airlines (that were first to charge for luggage), than on traditional airlines, because the budget airlines have much smaller carry on allowances.
On British Airways, Lufthansa, etc, I can take on board both a carry-on sized bag (in the locker) and a rucksack (decent day-sack size - under the seat if the lockers are full). I can live comfortably from these for a week on a typical business trip.
With budget airlines, I am only allowed one of these two bags (*). The other *has* to go in the hold. Therefore, I check in *more* bags when I fly with a budget airline than when I fly with a traditional airline. I think this is to extract more ancilliary revenue, not to reduce check in costs.
(*) I'm aware that some budget airlines claim to allow two bags. However, my *laptop* alone is too large to count as the second bag on Ryanair.
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easyJet toyed with the idea of "bring as many as you want provided they all fit in the sizer at the same time" - that seemed a really good idea to me.
It's not surprising they dropped that idea - it would have reduced their revenue.
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A better solution that doesn't come across as "money grabbing" would be to allocate a space in the lockers to each seat.
Indeed - but I suspect airlines rely on the fact that not everybody uses their fair share of cabin baggage space.