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Yes, however my opinion is that it may depend on when you got the first sign up bonus.
If that bonus was prior to this rule being rolled out, there might be a possibility to get another bonus. For example, if you got a PRG bonus in 2012, and cancelled the card in 2013, it might be possible to get a bonus in 2016. If you got the PRG in 2016, cancelled in 2017, seems most likely that you would not get another bonus in 2020.
There is also the possibility of smaller "upgrade" bonuses being offered. Open a Delta Platinum card for the bonus, close it. Open a Delta Gold card for the bonus. After a time, AMEX likely will offer you an "Upgrade bonus" for taking on the higher AF of the Delta Platinum again, a simple PC from the Delta Gold to Delta Platinum for 15,000 miles after $1k spend. I just recently went through this, after getting a Delta Platinum bonus in 2014 and closing it the same year.
My understanding is one and done, yeah. I've read a lot about checking for offers in an incognito browser window as sometimes they'll be higher (like it's been reported that ED, which shows the 10,000 MR signup bonus, will sometimes show 15,000 in incognito mode). May not always be the case for all cards but it's worth the extra look anyway.