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Actually interesting video! I'm clueless when it comes to fonts, but a few comments about the start (when he gives it some historical background):

What the Phoenicians did was to take a look at the hieroglyphs like, "Yeah! Love that! But... what if we made the symbols even more abstract?"

I know, he's oversimplifying it (as it is not the focus of the video), but it's worth noting that this abstraction was done by the Egyptians themselves, while writing hieroglyphs. Hieroglyphs often use something called the "rebus principle", where you represent a word by a similar-sounding word. For example, "son of" /sa/ was often represented with ⟨𓅬⟩, a white-fronted goose /za/ - because they sound practically the same.

(It's a lot like writing "I like The Beatles" as ⟨👁️👍🪲🪲⟩. Why ⟨👁️⟩? Because it sounds the same as "I".)

What the Canaanites (including the Phoenicians) did was to use this rebus principle in a more consistent way, and only for the first consonant of the word. For example, ⟨𓉐⟩ (a house) representing [b] because "house" in those languages usually starts with that sound. That's the start of the phonetic principle (graphemes represent sounds instead of concepts).

There's yet another level of abstraction, that it's hard to pinpoint when started to become relevant: instead of representing the "raw" sounds, you represent the underlying phonemes. It's the reason, for example, that the /p/ in ⟨pit⟩ [pʰ] and ⟨spit⟩ [p] gets the same letter - because although they sound different, they're still the same phoneme.

Now, there were a couple of problems with this early alphabet from the Greeks, there only had uppercase, and while they wrote in rows, sometimes they wrote LTR, sometimes RTL

Ah, come on, that's silly - neither is a "problem" of the lapidary early Greek alphabet. It's just the absence of a feature that he's used to, and the presence of another.

For comparison: this is on the same level as an Arabic or Farsi speaker saying "now, there are a couple problems with the modern Latin alphabet, such as lack of initial/medial/final forms, and writing the vowels with their own letters as if they were consonants."

Enter the Romans...

Further info on the alphabet. Be warned that it's mostly trivia.

• ⟨G⟩ is a later innovation, more specifically from 230 BCE. Originally the Roman alphabet used ⟨C⟩ for both /k/ and /g/.
• Including ⟨J⟩ was a mistake - it was not a letter back then, it originated as a curled ⟨I⟩ in the middle ages. ⟨I⟩ and ⟨J⟩ got "split" into their own letters rather recently.
• ⟨U⟩ was not a letter back then either, but he got it right. Same deal with the above, except between ⟨V⟩ and ⟨U⟩.
• ⟨K⟩ was only marginally used. You do see it popping up for native Latin words, but it's usually for Greek borrowings. Specially after Latin shifted /k/ to sound like [tʃ] (as in chill) before front vowels.
• ⟨Y⟩ was mostly used for Greek borrowings, representing the sounds [ʏ y:] (as in German Müller and über). Latin itself lacked the sound, and odds are that most speakers butchered those words to sound like [ɪ i:] (as in bit and beet) instead.
• ⟨W⟩ is not there because, although ⟨V⟩ represented three sounds in Latin, [w ʊ u:] (as in wool, book and boot), confusing [w] with [ʊ] was not a big deal (more on [u:] later). It wrecked havoc for Germanic dialects though, so they started representing the consonant with a digraph, ⟨VV⟩.
• ⟨Z⟩ used to be the sixth letter of the alphabet. Then it was kicked off the alphabet for being "too foreign". Then it came back at the end.
• Some Roman emperor tried to introduce three letters into the alphabet: ⟨Ↄ Ⅎ Ⱶ⟩, that were supposed to represent [ps w ɨ] (as in cops, wool, and Polish byt). They were mostly forgotten.
• The Romans used a diacritic, to represent vowel length, the apex. For most time it looked like its descendant (the modern acute), except over ⟨I⟩ - because then people wrote a longer ⟨I⟩ instead.