Yes, very important to get a home inspector, even for new construction. Our 1st new construction home was bought 5 year's ago and we did not get a home inspector. We will move into our 2nd new construction home soon, and this time I will use a home inspector (already booked). No one needed to convince me; I convinced myself. One hundred percent of new homes have a BUNCH of issues. This is no secret; the sales office of any builder and their construction site manager will readily tell you this. They will also tell you that that's what the walk-through and 1-year warranty are for. But these are beneficial only if you catch (or are not afraid to mention) every issue. But you won't catch every issue if you don't use a home inspector.
Example: My friend who was not a bio or other science major got a detached retina. I tried to tell him all the things you have to worry about and that he needs to ask the ophthalmologist a bunch of questions and then interview a few other ophthalmologists with questions about technique, instruments that will be used, probability of cataracts developing soon after (indirectly getting at the doctor's personal rate of avoiding cataracts), etc. He was scheduled for the procedure 2 days later and wanted to get it over with. The guy botched his retina reattachment, after which he started researching the procedure, found better doctors with better experience and better techniques, and got it fixed. However, fixing doesn't mean he got back the portion of his eyesight that he'd already lost. I see what he went through as almost the exact same as the home inspection. You're busy and stressed out, and you think it's better to be positive and hopefully everything will be fine (gambler's fallacy). And it's always, while looking back, you realize you were wrong.
There are technical issues that even if you did a ton of research on your own (like I tend to), you still might second-guess yourself (or you might be made to second-guess yourself by others) and think you're being picky or unreasonable. There are also other technical issues that you would never become aware of until many years down the line (such as Care's example of an AC unit that was too small for the house) when the issue finally presents itself. Or when you have difficulty selling your house because the buyer's home inspector discovers a bunch of issues you never even knew about. A professional home inspector covers all those bases.
I have talked to 2 home inspectors. The one I went with spent so much time on the phone with me to discuss 3 separate issues early on in the construction BEFORE I officially hired him (read: for free). His Yelp ratings are fantastic (and they appear to be real ratings). He is soooo detailed. His rate is too reasonable. This guy is a true expert (other guy wasn't even close). I already know (but I'll follow up after the home inspection, I promise) he's at the highest level of his profession--in experience, knowledge, and attention to detail. The name of the home inspector I'm using is Steve Lottatore.