I realize there are several similar questions, but i didn't see mention of the amount of deltaV needed beyond saying there is a slight benefit that is more than offset by dozens of social/political/economic factors.
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4$\begingroup$ FYI, the "launch straight up and then circularize" will cost you a fair amount of delta V compared to a more standard trajectory because of the Oberth effect. $\endgroup$– Charles StaatsCommented Apr 12 at 1:22
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4$\begingroup$ This makes no sense. If you launch "straight up" you will have no velocity in the direction that puts you in a circular orbit. You can't stop at 200 km, turn 90 degrees, and do a burn to orbital velocity. That's Bugs Bunny physics. $\endgroup$– Organic MarbleCommented Apr 12 at 3:56
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1$\begingroup$ The fast not high XKCD may be relevant here what-if.xkcd.com/58 $\endgroup$– GremlinWrangerCommented Apr 12 at 7:39
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2$\begingroup$ @OrganicMarble The astronauts just have to be careful to only look up so that they won't see the ground and realize they ought to be falling. $\endgroup$– Darth PseudonymCommented Apr 12 at 16:24
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4$\begingroup$ +1, good question and welcome to Space Exploration StackExchange. To the down voters: I don't I read this question as being an attempt to suggest a new engineering solution, I see it instead as a sensible step along the path of how to understand new concepts, by starting with an abstraction specifically chosen to deal with a limited aspect of the problem rather than dealing all the complexity up front. $\endgroup$– PuffinCommented Apr 12 at 20:40
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The Karman line is around 100 kilometers high and it takes around 2km/s to reach that according to Wikipedia, getting into LEO requires one to go around Earth at a speed of 8km/s, otherwise you will fall down on the planet. That is around 10km/s of delta V. Since mount everest is only 8km, it barely makes a difference compared to the 2km/s per second you need to get 100km!! And that is not even taking into accound that you still need to get to orbital velocity. In the end you are saving under a percent worth's of fuel making the attempt utterly useless.
To make matters even worse, if you fly up to 200 km before starting the circulising burn, then you make an even smaller difference. (Rockets do a gravity turn and do not fly straight up and then turn)
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$\begingroup$ Your answer could be improved with additional supporting information. Please edit to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers in the help center. $\endgroup$– Community BotCommented Apr 12 at 9:34
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$\begingroup$ What are some examples of rockets that fly straight up and then turn? You say most of the time they don't, so you must know about some that do. $\endgroup$ Commented Apr 12 at 12:16
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2$\begingroup$ @OrganicMarble Well I do not know any rockets that do that. I think you took it too literally $\endgroup$ Commented Apr 12 at 14:07
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$\begingroup$ Maybe you can count spin launch spin it is launch straight upwards and then flies sideways $\endgroup$ Commented Apr 12 at 14:08
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2$\begingroup$ @OrganicMarble You never flew an abomination into orbit in Kerbal Space Program?! :) $\endgroup$ Commented Apr 14 at 4:40