@snoMM1s - you are reading it wrong - seize the Initiative lets you go first in an initiative pass that you can act in. It doesn't increase your initiative.
"Move to the top of the initiative order, regardless of your Initiative Score. If multiple characters spend Edge to go first in the same Combat Turn, those characters go before
everybody else, in order of their Initiative Scores; subsequently, the other players and NPCs take their actions according to their Initiative Scores. This move to the top of the order lasts for the entire
Combat Turn (meaning multiple Initiative Passes); you return to your normal place in Initiative order at the start of the following Combat Turn."
In your example, if I have a 11 initiative, and my opponent had a 23, then normally:
Initiative Pass (IP) 1:
Him 23
Me 11
IP 2
Him 13
Me 1
IP 3
Him 3
I don't get to go
If I seize the Initiative, then it becomes:
IP 1
Me 11
Him 23
IP 2
Me 1
Him 13
IP 3
Him 3
I don't get to go.
Now, if I Blitz, I roll 5d6 in Initiative, meaning I have a higher initiative score, which does two things - it means that I will have more actions, and it means that my score will be higher so I am more likely to go first anyways.
Seize the initiative is useful when you HAVE to go first. Blitz is useful when you HAVE to be able to do multiple actions.