Not judging those who do, but I wouldn't use them on principle. As has been said, they take a large commission for providing very little extra. They forced their way into the market, relentless massive TV advertising campaigns, getting into people's heads so that they're what you think of when you want a takeaway and make you think it's the best/only way, but what added value do you really get - other than being able to pay by card, I suppose?
I feel the same way about the likes of booking.com and their ilk. They sell themselves on the convenience and often even the supposed savings, but after they've taken their own cut and thus forced the prices up across the board in order for the individual small businesses to be able to survive. Often, the margin they demand is all or most of the profit that a company will be making. A small B&B can either hand it over to them and then be bitterly accused of ripping people off when they have to put their prices up to survive, or otherwise not sign up and then lose out on the huge number of potential customers who've been influenced into going straight to the big central 'wrapper' website and no longer ever bother dealing direct.
A middleman should provide a valuable service for their money or ease something that would be difficult for you as an individual. If a shop sources a crate of 100 identical items in and sells me one or two of them, charging me significantly more than 1 or 2% of the cost to them, that's perfectly OK, because I can't use and don't want 100 of them and wouldn't otherwise have been able to negotiate with their bulk suppliers.
If a company with a fancy name and big marketing budget tries to convince me to contact them with my order instead of the takeaway and they then pass it straight on to the takeaway and take a massive cut for their trouble, inevitably sending prices up 15-20%, they're just parasites IMHO. They're no different from those scum companies that pay Google to appear first when people search for 'driving licence' or 'new passport' and transmit the data you input straight on to the DVLA or Passport Agency automatically along with the actual payment, having already charged you an extra £50 on top of that for them to keep for very little effort indeed.
Employees wouldn't be at all happy if their bosses kept trying to pressure them to get paid via Just Payroll, offering extras of dubious value such as instantly printing off historical payslip records or tax office information that's freely available online - and then never giving pay rises because they're already having to give Just Payroll an extra 15% on top of your salary and simply can't afford them. Why should small takeaways and other businesses be forced to sign up to Just Eat or otherwise lose their existing trade to others who do?