First off, price would not be 6-20 billion dollars. More like hundreds of billions of dollars.
You're talking about suddenly trying to purchase an amount equal to ALL the miners in existence, AND having to compete for these purchases with the existing mining industry which is always expanding, so prices of ASICS would go up. This would take wayyy more money than you suggest, and years to accomplish.
under all assumptions made by topic creator of lets say ethereum stakers selling off coin to purchase all batches of asics for X months(meaning no honest network growth)
current bitcoin honest network is averaging 600exa = ~2.56m asics

at a average of $6.3k per asic to get the performance needed of 2.56m asics. thats $16billion
(note there are other current range asics much higher cost/electric draw, but ill go with low budget prices)
then with the electric needed to run those asics, at a low planetary range of electric $0.04/kw = $14c/hour per asic
running a asic farm of multiple asics usually requires doing electric contract deals with energy suppliers of energy contracts of 6-24 months. usually 24 months to cover the ROI timescale
this is $2,453 of electric for 2 years per asic which is another $6.23billion. meaning in locations with the cheaper rate electric would be a hardware and electric cost for a 2 year lifecycle ROI expectation of mining of ~$24bill
if those wanting to mine in more expensive end of the planets electric rates ($0.50/kwh = $1.75/h per asic) this can become over $100billion for hardware and electric on a 24 month upfront cost