You asked me so:-
Most just multipurpose composts are made of 80 to 90% peat, peat by nature is sterile, thats why human and animal bodies thrown peat bogs are preserved for hundreds to thousands of years without decay. It is a medium that does not support life good or bad.
So near pure peat multipurpose composts, act very like an inert hydroponic medium as they have no micro heard and virtually nothing to support their life, its a hostile medium to them, like a human trying to live on the moon without life support.
Multipurpose with added JI, is in fact peat compost with added loam, loam is top quality top soil, a teaspoon of top soil contains billions of bacteria and fungi, its heaving with life, mixing loam in the compost brings it partly to life and changes it so its more supportive of life.
Inoculants are a mix of the best species of the micro-heard. For them to do well they need a good environment in pure peat they will decline and slowly die out, so reapplying would be needed. Even if mycorrhiza makes symbiosis with plant roots, the peat contains little or nothing to sustain it. So to get the best out of inoculants they need a medium that supports them.
To support and sustain the micro heard a medium with every thing they need to grow and be healthy should be in the mix.
If you start with peat a dead substance, things that can be added that bring it to life adding loam, rock dust, worm casts, rotted manure all support and sustain and add microbes.
Do seaweed extracts (maxicrop or vitax) or fishmix act as a basic inoculants?
No, but used on soil or a living compost they support the micro heard!
Biobizz say their grow has bacteria in it, is it effective watered into an inert medium? No!
IMHO if you want to use straight cheap peat composts, you are better off using chemical fertilisers.
Edit to add to understand more about soil have a read
here, its mostly correct, a really good compost does a similar job to that of soil in a container or pot.