A little looking around points to global plastic production being near 370 million tons. By comparison, global seaweed production is near 10 million tons, wet. Trying to expand seaweed aquaculture 37X is not very likely, and would have many negative ecological effects. Existing seaweed production is already in high demand, and cheap plastics are not a likely endpoint.
Basically, the biosphere is not capable of replacing fossil fuels on the scale they're currently used. Corn ethanol can't replace gasoline, soy oil biofuel can't replace diesel, seaweed plastic can't replace natural gas petrochemical plastic. There's just not enough to go around, and the costs - in area, in fertilizer, in processing energy - are just too high.
There is a solution, it's industrial-scale renewable-powered direct-air-capture-and-reduction of atmospheric CO2, plus water, to hydrocarbons from methane to jet fuel (including the plastic precursors). It doesn't require arable land - a desert wasteland bordering an ocean would be a perfect location.
I don't, the ocean is a big place and we haven't seriously started to farm it anywhere near it's full potential yet (bet we do before long though).
Now granted many areas won't be suitable for seaweed cultivation, but if the demand is there, humans can get really innovative. The thing is, we don't make plastic out of seaweed yet and likely won't until we have to, and maybe never at all.
I do like your other idea better though if feasible. Save the ocean farming for food.
It's rather backwards to pull CO2 from air - with all energy required - just to make it the jet fuel. Instead, stop running jets - except very exceptional, or some hydrogen-based, move to propellers - most jets are subsonic anyway, and move from regular plastics to biodegradable ones.
This article is about the latter. 37X looks surely tiny comparing to how much we need to scale CO2 atmosphere scrubbing...
I've noticed that packaging for consumer goods accounts for a sizable portion of waste. This is something that could be curtailed even without innovation taken into account. Some sort of policy decision will be necessary as it will not suffice to deflect responsibility to consumers, especially when that demographic is only growing in the West. We can't outpace growth with shaming.
There is nowhere close to a research consensus agreeing with you - this is a very open question still. There are certainly a lot more reasons to be skeptical of a direct-air-capture industrial solution scaling though.
Any source that does not look at the benefits of a circular economy of kelp farming (producing more fuel and plastic to build the next batch), as well as upwelling tech (bringing nitrogen from the deep sea to the surface) is missing key facets too. It's very plausible large swaths of the ocean with little life currently could be turned into viable kelp farms (great for fish and life) which pay for themselves sinking CO2 by selling excess fuel and plastic. Demand is more likely to be a problem than production. If only we could think of some useful things to do with endless dirt cheap biodegradeable plastic. HMMM
Kelp and biological sources of CO2 drawdown (bamboo on land) are much more cost efficient, environmental and scalable than any industrial drawdown process currently known.
Basically, the biosphere is not capable of replacing fossil fuels on the scale they're currently used. Corn ethanol can't replace gasoline, soy oil biofuel can't replace diesel, seaweed plastic can't replace natural gas petrochemical plastic. There's just not enough to go around, and the costs - in area, in fertilizer, in processing energy - are just too high.
There is a solution, it's industrial-scale renewable-powered direct-air-capture-and-reduction of atmospheric CO2, plus water, to hydrocarbons from methane to jet fuel (including the plastic precursors). It doesn't require arable land - a desert wasteland bordering an ocean would be a perfect location.