It's not a "team" thing, and I reject wholly the implication that anyone opposed to this is just trying to score political points for their "team." Perhaps people twisting the narrative to "they won't let anyone read the laws!" are indeed politically motivated, but that's not what you or I are discussing here -- and even so, you need to assume good faith if you want a discussion.
While it is reasonable for LexisNexis to be the official provider, it is not reasonable for them to abuse this privilege by charging silly amounts for certain kinds of access, and it is not reasonable for the state to sue to prevent others from distributing copies of what should by all rights be public domain and fully accessible material. Those problems are what's at issue here, not whether or not the state can hire a DB administrator.
1.) gives them right to force you to remove links to the content (section 6.b)
2.) gives them the right to advertise while showing you the law (section 8)
3.) does not require the provider to have accurate text, or be free from malware (section 11)
4.) requires indemnification (section 18)
5.) requires that the jurisdiction be New York (section 22)
6.) terms can change at any time, for any reason, without notice (section 26)
7.) cannot be used for commercial purposes (section 2.1)
8.) nor make a copy (section 2.1)
It doesn't cost any money to access it online, but the limitations on actually using are very real.
Want to provide a link to it via a blog to educate your local neighborhood? Want to know that the official law is free from errors? Want to use the law, but hold the provider accountable if the information is grossly incorrect? Want to sue the provider in Georgia since that's the official law? Want to know that the terms of service stay consistent from day to day? Want to use the law to help your business succeed? Want to provide a copy of the law to others so that they can educate themselves?
All of those items are restricted in some way by these terms of service, which are required before access to the law is allowed.
Without the annotations, you do not have the full law.
It seems like some folks may not like that a private company does the hosting or that they have exclusive rights to its reproduction. You could consider some reasons this might be the case that are reasonable, like the cost of maintaining it is actually cheaper by having a company who has the appropriate resources and infrastructure to support it, it's probably a challenge/costly to hire an internal team to maintain it at a high enough quality level, the hosting company made a deal with the government to reduce maintenance and hosting costs by having exclusive hosting/reproduction rights. These are all pretty reasonable things to happen,given that the source text is still freely available to anyone. I think anyone who has an argument against this is probably looking for a reason to get upset at what they perceive to be unfairness by "the other team", and won't be convinced otherwise. Such is life, oh well.