Forgive, I'm going to be rearranging quotes from your question.
So would you buy the 6D having only the nifty-fifty lens?
... given current prices of the 6D this might be my only chance of getting into FF.
No, I would not buy the 6D, not if cost is an overriding factor, and I'm already having trouble putting together the budget to purchase a used 6D body. The 6D is low-cost because the 6DMkII is out. How much lower will it be when the 6DMkIII is released? Go look at the prices on the 5D "Classic" (Mark I) or 5D Mark II. This is far from being the only opportunity or choice for an affordable full frame body.
And in the meantime, you have to save up for glass.
... but I can buy other FF lenses later on.
Yes, you can, but have you looked at the prices? The kit lens for a dRebel is the EF-S 18-55 lens, roughly $250 new, but sub $100 used. The kit lens for a 6DMkII is the 24-105L. Which is roughly $1000 new, and around $700 used.
Full frame glass requires more glass. And will typically be higher-end than crop glass, because who wants low-end glass on a full-frame body? :) The full-frame lenses you're likely to look at are all going to be more expensive than their EF-S counterparts. That 10-18's FF equivalent is a EF 17-40/4L or EF 16-35/2.8L. The full-frame kit lens is a 24-105 (L or STM). The 55-250 IS's equivalent is the 100-400L.
Remember, all your glass gets 1.6x shorter in the move. To get the FoV equivalence of 250mm on crop, you need a 400mm lens on full frame. And that 50/1.8 STM of yours? It's gonna look a lot like a 35mm does now on your 700D. You may want to replace it with an 85/1.8 USM for something closer to what you're used to with the 50/1.8 STM now.
Every lens you have can change in usage when you switch format, just because of the crop factor.
... even in broad daylight full frame photos seem to be sharper, more clean and rich than from a crop.
Consider that folks who spend thousands on a new full frame bodies may also be the kind of folks who spend thousands on L lenses, and have the experience, talent, creativity, and exposure and post-processing capabilities to make the most of any scene they capture. Not to mention the sheer-minded bloody determination to buy airline tickets, scale mountains, and get up at 4am to hike miles to the best vantage point in the best season to get a stunning landscape shot. It's not just the sensor size that may be different.
Are you shooting RAW and using Photoshop or Lightroom? Are you shooting with L glass? Are you off-camera lighting? If not, I'd say pursue those before a full-frame sensor, not only because they can be much cheaper, but will include improvements and purchases that will travel with you if/when you make the full-frame leap while being great with your 700D right now.