Switch is 13.9 mm thick. However, I think it should have been around 30 to 50% thicker. The joy-con would be thicker as well.

Here my reasons, which I divided on pro points for joy-con, pro points for the main unit, and con points:

The pros:

On joy-con

• Joy-con drift: Yeah, the main build issue of Nintendo switch would have been solved if switch was thicker. Switch is the console with smaller volume of the analog sticks box compenent. So, they had many restrictions building it, what caused the issues on the analog stick box, what caused the drifts. If they had more space, they could avoid this issue entirely.
• Joy-con communication issues: Early joy-con had communication issues with the main module because of the weird positioning of the communication antena. Fitting a small space was the reason. 
• Joy-con wabbling: Yeah, there are complaings about joy-con wabbling when attached to switch. If it was thicker, the contact area of the trails would be broader, and it would feel solider in hands.
• Ergonomy: Joy-con is very small, many have incredibly difficulty to hold in hands, in very ackward positioning. If it was a little more thicker there would be more space for holding on the side and back, and could be a little less difficult to hold for big hands. Also, It give freedom for have rounder edges, making it more ergonomic in general, even when attached to the main unit.
• Joy-con battery: With larger physical space, there was the opportunity to fit a larger battery, and therefore, more time playing without needing to recharge.
• More gameplay capabilities: The right joy-con has features that the left dont have, space limitation might be one of the causes. This fact impacted the gameplay possibilities for some games. For instance, we cant have multiplayer games that use the infrared sensor on both joy-cons. Also, more features could have been implemented, like audio output.

On the main unit:

• Larger battery: More physical space for fitting a larger main battery, a common issue users complaing that could be better.
• Better cooling system: With increased internal volume, there was possibility for better cooling system.
• Games look better: As consequence of a better cooling system, the clock could be pushed harder on the handheld mode. As the development of games is limited by the handheld mode, they have this configuration as development base. If the base configuration has a higher clock, and therefore, is more capable. 

The cons:

• It would kinda lose a little of its sleek design. However, it doesnt seems that this is a significant selling point.
• Would be bigger, bulkier. Harder to fit on spaces. Switch Lite wouldnt be that Lite. But 30~50% might not be that significant. Still less thicker than gameboy or folded 3DS. 
• Joy-con grip would have to be different. Same for the dock. No big deal.
• Increased weight. Maybe the most significant issue.

Given the pros and cons, I consider the pros are far more significant. Therefore, the Nintendo Switch would indeed be thicker. Yeah, some bold speculations, but still.

Thoughts?

I like my handhelds like I like my women. Thick as a brick baby.

I kinda wish they were able to get a Tegra X2 and 6GB of ram but I guess it would not have worked at $300. As it is now, give me folders and themes.

Nin apparently likes them like their coffee and woman. Crisp and thin.

An area perhaps where the Japanese should take a page out of the American's book. Just not the fast food section.

Another con and the most significant one that likely shaped most decisions in that area are the costs. It would be more expensive, especially with bigger batteries and cooling system. They wouldn't have been able to sell it for $300 anymore.

I think you're right, but probably looks cooler for the general public this way. The Steam Deck, as many advantages it certainly brings, doesn't look that attractive, for some reason. Most mobile thingies today are very slim, it could be that. Also, in my experience, the size is perfect for children. I've heard of a few that don't like it and would prefer it bulkier, but most are satisfied with the setup. Not sure about what you've seen.

However, if some of the problems you bring up could get fixed with a thicker unit, I'd certainly vouch for it. Ergonomy is not much an issue to me because that can get fixed with cases, and there are a lot of options for those. You can get elegant dockable cases that offer decent comfort but also allow you to remove the Joy-Cons whenever you want like Supcase's, or you can get cases that offer interchangeable grips, like Skull & Co's.

EDIT: Thanks, dude, I needed a Switch waifu. 

It was already big for a handheld. I'm sure the last thing anyone wants is a handheld much larger than the Switch.

I do wish they had made the joycon connectors stronger though because after wear and tear the controllers do sometimes get disconnected from the system when playing in handheld mode.

I fucking loved the OG DS. If I ever ran into a tough situation it could double as a weapon.

The screen broke easily, though :( After three years, mine was dead, and really never treated it awfully, so it came as a shock.