Why doesn't Mike Ross just get a law degree?

Everyone has mentioned one or more of the reasons but not all of them in one response.

1. Getting a law degree now opens more opportunities to be exposed and ultimately equates to rearranging the deck chairs on the "Titanic". His career is finished and the only questions that remain is the terms of the sentence.
2. The whole premise of the show is based on this and it is one of the cinematic/dramatic elements that maintains a varying level of tension to series which the writers alternate levels of attention to when it looks like everyone is too comfortable and think someone could really get away with this and be in the spotlight. It is only a matter of time before he is caught with so many learning the truth, so many LSATS for others, and ultimately the lack of reporting consistencies that exist between school records and actual records which are paper trails that are all suspicious. Health and immunization records or the lack thereof while protected legally could be one of many nails used in the box of inconsistencies if anyone needed to go beyond no professor or alumni recalling his presence.
3. Being able to practice legally anywhere else beyond the "Rome" itself as New York is the center which all legal roads and high ground lead, is anticlimactic to the character who has now exchanged his drug of choice for even greater high wire thrills of performing without a net. Also, see reason #1 as this does prevent him from going to prison but potentially allows him to avoid being exposed as quickly if it didn't raise more red flags than it avoided. Who wouldn't dig into the history of a successful lawyer leaving a top firm in New York unless they were hiding something? (This plot is covered in the newest episode, where another PARTNER wants to reward Mike with a junior partnership, elevating their non-HARVARD-educated lawyer into a position of prominence in a firm known for hiring Harvard grads ONLY. He can't accept, but also cannot refuse, but he also cannot leave, since all would be weird responses to this honor.)
4. Leaving the law or no longer committing future felonies does not prevent past ones from catching up with him as the series experimented with his departure for other high paid employment which touched on past issues coming back regardless of his career change.
5. Human motivations are categorized as actions that fall under two main categories of fear and greed. Seeking pleasure or avoiding pain is the underlying motivation for most decisions. Having gained so much and seeing no way to avoid devastation from previous damage, the only option in his mind is immersing himself in the pursuit of pleasure both financially and emotionally in his relationships and his practicing law.

I'm sure there is more that can be discussed but I think this as comprehensive a list of reasons why he chooses to move forward without trying to legitimize his continued practice despite a mountain of ever growing future legal disasters for everything and everyone he represents.

Getting admission into Harvard isn't exactly easy. Mike is working in a firm that hires exclusively from Harvard, and he has spent years building up his reputation in said firm. Not only will he not be able to rejoin the firm as Harvard would not grant admission to someone with a history as shady as Mike's, he may not be allowed to practice law in the first place, once it's revealed that he was practising the law without a degree.

In summary, it is now irrelevant for Mike to have a law degree, as the act of acquiring one will cost him his job. If you ask why he did not get a job before: don't forget that he wasn't exactly clean before Harvey took him in. He regularly used to do drugs, and never really thought about his future. Joining the firm under false pretences was an impulsive decision that benefited Mike in the long run, and wether he likes it or not, it's a decision both he & Harvey have to live with, now.

I think they explored this question on the series, but basically the answer is that he'd have to practice in (from his perspective) a backwater town like, SHUDDER, Atlanta, for example, and he wouldn't be at the Olympic level of New York law.

In short, he could, but Mike is too arrogant to accept anything less than being at the very top of the game.