Over the short term yes Litecoin could do very well if Bitcoin seizes up even more due to the 1 MB blocksize limit; however from the long term fundamental point of view Litecoin has the same issue as Bitcoin. Think Bitcoin with a 4 MB blocksize limit. This only kicks the can down the road.
By failing to account for the effects of the Lightning-type payment channels which segwit enables, your scenario assumes (within circumstances which may be avoided) facts not yet in evidence.
With segwit LTC already quadrupled its effective block size once, so what makes you think they couldn't do it again if/when necessary?
PS Bitcoin has not seized up for anyone paying market rates for priority processing. I've been particularly pleased with the next-block confirmation and very low fee of withdrawals from Poloniex. "Seizes up" is just your intentionally inaccurate, technically meaningless FUD phrase; it's merely a provocative, emotionally laden term falsely implying Bitcoin is not working within established functional parameters.
Thanks for getting me to look up the origin of the Bitcoin Paralysis trope; Gavin's May 26, 2015 article "Analysis Paralysis" fairly epitomizes its genesis.
Note the date of Gavin's post is May 2015, which was more than two years ago.
Now focus on the insinuation in Gavin's conclusion:
I don’t think we should adopt the Silicon Valley mantra of “move fast and break things.” But I do think we need to move– “stay still and watch things break” is just as bad.
Gavin's entire point was that the "Core Bitcoin project has been suffering from analysis paralysis over the block size issue for at least three years" and that it will break if we don't embrace his vision of a contentious hard fork.
But that prediction was wrong. Very wrong. Bitcoin in 2017 works better than it did in 2015.
As a fellow man of science, presumable subscribing to the philosophy of empiricism, how long are you willing to tolerate Gavin & Co's failed doomsday predictions before you reexamine and reevaluate their hitherto unvalidated models?
Of course absence of evidence is not evidence of absence, but IMO you are falling for what Prof. Szabo calls Pascal's Scams.
http://Http://unenumerated.blogspot.com/2012/07/pascals-scams.html explains why the Gavinsta "hardfork right meow or d000m!11!" scam and global warming, etc. are parasitic memes feeding on artifacts of human (ie not strictly logical) cognition.
The Chicken Littles have been wrong for 5 years about Bitcoin's sky falling absent a contentious hard fork. That half decade of experience has provided reams of new evidence and information about Gavin/Hearn's "Bitcoin has failed" hypothesis. Time to adjust your Bayesian inference accordingly.