Do you want to pay $16.5, $17.9 and $19.3M for Rudy Gay over the next three seasons? I sure don't. They already said that Sterling doesn't want to pay three max players in relation to Dwight being teamed up with Blake and Paul, so why would be pay a vastly inferior player?
Having Gay would give the Clippers a "big three" contract wise, but not production wise. This would mean that the roster would have to be rounded out with cheap players because Sterling isn't paying luxury.
Blake next season: $13.7M, Paul ~$18M + Gay = $49.6M
If the team traded for Gay, it basically means you are trading whomever you give up+Paul for Gay because Paul will not be re-signed (he might not want to return to such a cap situation). Paul + Blake + Rudy would be about $49.6 million of the cap taken, and increasing every year. If DJ was supposed to stay in that trade, then you would have 4 players putting you at about $61M. add Jamal Crawford, $65M. So there is a $6M gap before luxury assuming it is $71M next season.
Not happening for many reasons with the most important being that it doesn't improve the team since you would have to cut costs in other places. For example in a trade for him, you had Gomes/Butler/Bledsoe (8+4+1.7 = $13.7, +$2.8M, don't even know if the trade works money wise, but assuming it does).
The next season, to re-sign Paul and stay away from lottery, you would have to let Odom and Billups go. For this season, hope Billups is back early and you play Odom as backup SF because you still don't have on and have increased the payroll by almost $3M.
You could try to build off that next year, try to fill 7 roster spots with $6M. Add Thompkins and Leslie and it is 5 spots with $4.2M. That means time to go shopping in the second round. Trade 1st round pick to a team for two second round picks.
Paul / Cheap FA PG
Crawford / Leslie (0.9K)
Gay / 2nd Rd Pick
Blake / Thompkins (0.9K)
DJ / 2nd Rd Pick
With DJ's contract on the roster, no other high priced player can be added to Blake and Paul while having an owner that isn't going to pay luxury. Even in the above scenario, as they get their yearly raises, the team will go to luxury. Or you try to trade Crawford, then start Leslia? at SG. Worst bench in the NBA.