"well basically" is correct and usable in written English.
It is used to introduce a thought or opinion in a casual way. For example, "Well basically, I think this issue is too complex to easily solve."
Being cynical and getting annoyed with basic humanity is, well, basically human.
"Well, basically that is dead.
— Well, basically I liked it, but it definitely dragged.
If not, "it became a matter of … well, basically digging.
They are very strong – brought up well, basically.
"Well, basically, it was stupid and I did it and whatever," the defendant said.
Dallasharriet44: George and Laura... well, basically they're really cool but their daughters don't know it!!
"Basically?" "All is well, basically," he said, hearing her honest concern.
Well, basically because it's the central insight of Keynesian economic thought.
Well, basically, anything you'd use for sushi: avocado, which is incredible.
"Well, basically, I think you just communicate until your knuckles bleed".
