Lawyers, by reflex, attempt to insert themselves in the middle of processes, and naturally tend to create conflict. (This is according to my experience, and the experience of many others.) If a lawyer can do this, the negotiation will naturally take longer, generating billable hours.
Secondly lawyers all know that the person who is in a hurry to get a contract is going to get a worse deal, and so will NEVER be in a hurry to close the deal. But there are times when "winning" this negotiation is simply not worth the delay.
Now step back and look at it from the point of view of a company. Paying lawyers fees is not good. Creating conflict with someone you want to cooperate with is not good. Making negotiations take longer is not good.
Making this concrete, I was in a recent negotiation for a pay for performance compensation. Because it was pay for performance I could quantify how much delays cost the company versus what I will get paid. Their lawyers' delays cost them several times what I will get paid. On my side I did not let my lawyers negotiate. I told them to identify everything in the drafts that I should object to. Then I negotiated without them. Once there was nothing that made me unhappy, I signed. And what I got was pretty much the deal that we agreed to up front, in person, which I emailed to them months earlier.
Limiting my lawyers' role saved me thousands of dollars. If the company had limited theirs, they would have saved thousands of dollars. And would have had a contract faster.
TD;LR, just because your lawyers want to be involved, and try to convince you that they should be, doesn't mean that they are providing value.