The issue people have with plastic buckets is really only IF you are using one that is not foodsafe.
Buckets as primary fermenter are particularly popular with winemakers ... I don't do much brewing and so I can only speak to vinting. The oxygen exposure is crucial to getting yeast going and the bucket fermenter (with a piece of cloth draped over the top to keep fruit flies and other debris out) is a great way to get the ferment going.
Bucket fermenters are just a tool and whether they have too much headspace to be used past primary fermentation is up to the individual. Some do put the lids back on and put an airlock on thru the lid to use as a secondary fermenter. I do not, as I think it's a better practice to avoid that large open surface area in the secondary even if you do top the bucket up to withing a half inch of the lid.
"Bucket" style fermenters run all the way up to 30 gallons+. The most common large open top fermenter is the Brute Rubbermaid garbage pail. These, like other large "civilian" fermenters are marked with the NSF logo which indicates they are suitable for food use. Restaurant supply places and even Home Depot and Lowes have large open top buckets and pails useful as fermenters in a range of sizes and mostly for reasonable prices ... just make sure it's got the NSF logo.
Alternately, some fast food places still get food in 5 gallon white food safe buckets ... Burger King comes to mind and I've had great luck with them and have gotten more than 30 of them from the kind folks at BK's. Jimmy Johns Sandwich restaurants use a 6 gallon bucket ... a nice size.