I disagree with this, despite having no proof of the algorithm the airlines are using to assign flight numbers. While it's a complex process involving phonetic separation, eliminating two simultaneous flying flights, and providing some code-share divisions, the carriers are definitely playing into the DOT's tracking schemes. See this article for example.

The DOT delay playbook:
--Schedule often-delayed flights under regional carriers
--Adjust times and flight numbers to avoid delay tracking (DOT only reports stats on flights with 10 or more flights and delayed for 2-3 "consecutive" months in the report)
--Break your regional up into smaller, untracked airlines (even better!) as SkyWest, Envoy, and Expressjet are the only ones left reporting. This leaves Shuttle America, Endeavor, Compass, and GoJet to soak up the delayed routes on DL connection.
--Replay the DOT stats (as required and when beneficial) on the website. Avoid reporting your own on-time stats, only those reported by DOT and use those in your advertisements and news reports. (i.e. DL ranked number one "Based on DOT Air Travel Consumer Report statistics for domestic flights 11/14 for flights flown and compared to our competitive set. Competitive set is among major U.S. carriers: Alaska Airlines, American Airlines, JetBlue Airways, US Airways, United Airlines and Southwest Airlines.")

Airlines like Southwest that don't codeshare often end up bottom-barrel in these rankings.

The DOT Fly Rights says that the airlines must report the on-time stats, put a "special notice for flights that experienced serious delays or cancellations", and to check the Air Travel Consumer Report for chronically delayed flights.

Let's now look at DL's 7PM SFO-LAX flight, operated by DL (thus reported to DOT as compass is ignored).
From delta.com:
On time: 16%
+30 mins: 72%
+60 mins: n/a
No special note
Also surprising, there's no entry in the ATCR

Reporting 72% +30 mins, not in the chart

Last month it was 2764
Today this is flight 2770
In September it's 2777
In October its 2766
"For reasons not related to operational reliability" seems hard to buy

Now we won't have this flight showing up in that pesky consecutive delay chart no matter how bad it gets.

So what happens if DL messes up and shows up in the nasty chart? Let's take a look: BOS-LGA in Feb/Mar
The 6PM BOS-LGA DL 2689 , late +30 minutes 86% of the time in Feb/Mar. Off the naughty list in April, probably weather related. So now it's 2740 as a codeshare on untracked Shuttle America.

What about the 530PM DTW-EWR
DL388 in December
DL1794 in Jan at 535
DL4691 in Feb at 541
DL5346 in Mar at 525
DL2514 in April at 540
Operational reasons? Could be, sure. But it helps to have high-delay flights bouncing like that.

It's just conjecture of course, but if I was operating under these rules, I'd optimize around avoiding DOT delay lists, wouldn't you?