The union objective in the east being to either force Lee’s army into surrendering or capturing Richmond. How does proceeding to New Bern 217 miles away (according to google maps) proceed any closer to achieving the afore mentioned objectives? Lee wasn't going to follow him into NC, knowing that DC was exposed.
One of the interesting questions here is what exactly would Lee do if such a campaign came sweeping up from below? We don't have the exact details of such a plan, but the concept would be to leave a strong enough force in the significant Washington forts and attack the Richmond\Petersburgh supply lines from below. The idea was to force Lee to defend those lines or lose Richmond - which would get Lincoln reelected and continue the war.
The problem with that plan, of course, is the unpredictable tactical ability of Lee and the ANV, and the obvious stumbling that comes with large supposedly great multi-pronged plans. Coming from the south would leave Lee the initiative - even if he had to defend Richmond - and it's an open question how well Lee could have shifted resources and made moves that might have resulted in USA lost battles, blunted forays, or panicky redeployments. All the Looks-Good-On-Paper campaigns have a common tendency to unravel, and Lee was still a master unraveller.
Lee with the intiative and interior lines was dangerous. Period.
An Overland campaign was going to be brutal in any realistic assessment, but it had the advantage of taking the initiative away from the ANV, keeping up a constant grinding contact and slipping to the flanks, controlling the flow of the battle while wearing down the foe. If the AOP got the ANV in an open field battle, that's a battle Grant will take every time. If the AOP gets between Lee and Richmond, that gives some intuitive back to Lee but gives him little time and space to act on it (as well as interdicting supply, etc). If the campaign ends with Lee besieged in Richmond (or the equivalent Petersberg) then the siege will be longer and bloodier but will eventually bag both.
So the Overland Campaign does make some sense, even more so if the planned flank attacks had performed half decently. But that's a whole other thread.
Personally I'd reserve judgement on the 'coming from the south' plan until we saw more concrete details of the actual design (which we don't have). And remember, perfect On-Paper campaigns never survive contact with the enemy....