Pretty sure it does have a fan:
But yeah not as good cooling is the only reason I can think of for it not being compatible. Don't see any other reason to not support a dock, it is a shame. I mean it probably can't physically fit into the current dock, but they could always release another dock or an adapter/cable for the current docks. Dropping support for video output isn't going to reduce production costs.
Marketing and maximizing profits are reasons to not support a dock. While in the past I had proposed a handheld-first Switch with optional dock purchase, it's an idea that is not as easy to market and comes with the problem of allocating shelf space to a new dock because the different size of the new SKU necessitates its own dock. There's also the issue of potentially devaluing the standard SKU, but the plan is to offer both models side by side and have both of them sell as well as possible.
While Nintendo does have an error on their website as far as confusion about Joy-Con compatibility is concerned, it's overall easier to market handheld-only than handheld-first despite the console's name. Switch Lite is a Switch that can't switch, but in the end the market is probably not going to care about that too much, because the feature to switch isn't necessarily mandatory in any given purchase decision and will probably be completely irrelevant in many cases.
When it comes to marketing, do you think it would be more difficult for them to communicate that a dock is sold separately, than that it can't dock at all?
If so, why?
For people who know little/nothing about Switch, they may not expect the docking feature, so it won't matter to them.
Though if they are curious why it's called Switch, I can see how this can lead to confusion in some cases if they look up info on the wrong Switch.
For people that know how the original Switch works, this can also lead to confusion upon purchase. Unless they read Nintendo's description of how it can no longer dock. In which case they could have read about how docking is sold separately.