The base math of the game assumes every character will have three good stats: a primary to-hit stat, a secondary stat based on their build, and a third stat for their last defence.
No it doesn't. If you look at the base math of the game you only get 2 improvements per stat boost. It assumes you
can not have three good stats.
The game assumes an 18 in their primary stat and 20s are common as well,
Nope. The game math was balanced round a
16 in your primary stat. It's just that players more frequently go for 18s or even 20s.
And it assumes you'll out every stat boost into that same state and your secondary stat.
Once again, nope. It assumes you'll put your primary boost into your primary stat. In other words you get better at what you spend a lot of time doing. Splitting your secondary boosts
works.
All characters are optimized for one of four combat roles.
Because a two weapon ranger does
exactly the same thing as a sorcerer. Riiiight.
All characters can innately participate in combat and be effective.
This, at least, is true.
4e characters are built very much like optimized 3e characters who focus on a single role and put all their skill ranks in the same skills every level and always take combat options.
Nope. 4e characters are built like non-min/maxed 3e characters. You don't worry about long feat chains, unlike a min/maxing 3e fighter. You don't have an incredibly long spell book and the ability to do almost everything, unlike a 3e wizard or cleric, and don't trawl the bestiary, unlike the 3e Druid. All your skills rather than just your hyper-specialised few grow as you level.
Your claim you focus on a single role is in direct contradiction to the rulebooks - and to effective play. For instance my last Warlord was simultaneously able to restore hit points, able to tank one flank unsupported (as he frequently needed to do) and when swearing at the monsters he, as a Bravura Warlord sometimes used to top the DPR lists with Brash Assault and Provoke Overextension handing out free attacks on his turn (although not when tanking).
So once again false.
The base of 4e is a minimum level of optimization. "You need to be <this> optimized to ride 4th edition."
Where the minimum height requirement is one a teenage halfling or gnome would pass. "Work out what you want to do. Pick a class that fits it. It has a primary stat. That should be your best. Then build to whatever theme you chose."
Jonathon Tweet has also been engaging in edition warring it seems.
I see no edition warring there. He says what he thinks worked and that he found it disappointing. Which is fair enough - there were a lot of bits of 4E I find disappointing. He's as allowed to not like it as I am to not like his version of D&D. He's also talking about D&D Tradition rather than D&D itself. Which is ultimately a huge difference. If you claim that 4E is not D&D you are objectively wrong and being offensive at the same time. If you're talking about D&D Tradition then who cares? Some people, evidently. But D&D Tradition is not the same as D&D.
That was a fair and measured piece from someone who does not especially like 4E but recognises it has good points. There is nothing wrong with that. He's not trying to pass off untruth as fact, and he's not trying to kick 4E out of the D&D family.
Edit: There was also the line about 4E limiting the characters you could play. He was IMO incorrect there - but one of 4E's core problems was that it wasn't obvious about how you did things. IME 4E limits characters less than 3E - but you need more system mastery to play offbeat characters in 4E rather than being restricted by being punished by the game rules.