Opinion on this subject seems to be divided. I think overall the grass needs to be quite short & actively growing. If the grass is long it won't breakdown &you end up just trailing it into the house etc.
I have a Stiga mower with a mulching plug. Usually it takes about 4 hours to mow my lawns removing the grass but only takes half a hour with the plug in. Yes it needs to be kept short but it's so much easier that I can happily do it much more often without the faff of disposing of grass. I haven't found it creates thatch any more than walking on the lawn and it does feed the lawn. Having said that, I will sometimes mow without the plug so I can add cuttings to the compost bins. If you're worried about thatch, how about using a lawn rake maybe once a year.
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I'd google it and find a film on you tube