They already make Inmarsat (BGAN)/Iridium WiFi hotspots. This would be no different. Power and view of sky go in, Internet comes out.
What about rainy clouds and thunderstorms? While i want to be outside in sunny weather and work on my laptop during rainy day - that's when the connection quality is worst?
Heavy weather will almost always diminish satellite connectivity. Will depend on what Ka/Ku bands will be used between satellite and terminal.
Those antennas are extremely expensive and large, so the OP's dream is largely just a dream.
Google image search "iridium hotspot" and "bgan". They range in size from a small ipad to a large ipad. Pretty reasonable for global connectivity (although not built into a laptop's frame).
Those small iridium hotspots are also much lower bandwidth
2kbps to be precise
And the starlink antennae they "hope to get down to the size of a pizza box" (which also of course needs to be powered). This is not a mobile solution.
If I can fit it in a pelican case in a checked piece of luggage (62 linear inches, up to 50lbs), it’s mobile enough. Carry on luggage compatible would spoil me.
They also weight 800g.
You missed the "expensive" part, and iridium is not comparable when looking at speeds.
The target price is (was as of 2015) $100-$300. Really not that expensive.
The target price means nothing. Musk hasn't talked about them in years. Other companies have tried (and failed) and low cost phased array. Until they're delivering at that price, think of it like musk's original Tesla production rate predictions.