The busyness of serious Mormons (specifically Mormon men) arises naturally from the three life priorities of family, church and work.
Families are the priority. There should be as many children as can be raised decently; and families must be given adequate time and energy.
The LDS church absolutely depends on members to run it, and good works are mandatory. There are 'callings' to numerous necessary specific part-time, unpaid church jobs (of which the heaviest may be Bishop and Stake President, but many are very time-consuming, and at unsocial hours).
Work for Mormon men must be harder than for most people; because there is a tithe to support the church, a larger than usual family (indeed, the family should ideally be grown until it uses-up all surplus income), missions to be saved and paid for, more education than usual to be paid for. And this means the added busyness of careful, detailed budgeting.
In sum, to do all this; active(devout) Mormons almost-must be busy- and by all accounts they are. Very.
This is as it should be; this is the way the world runs.
And most people seem happier to be busy - and being busy at good things is the best kind of busy - and I say nothing against it.
Busyness has a cost, of course - in terms of depth, contemplation, originality, spontaneity... but it probably is a cost that is (nearly always) worth paying - at least the good things of life - family and church; and also work, and therefore 'society', are beneficiaries of the cost paid.
But for myself, I cannot tolerate a life of busyness.
I have tried, several times, and failed to lead a busy and efficient life - but I simply cannot make myself do it.
Like Thoreau, but probably more so, I absolutely require a life 'with a broad margin'.
If I am not getting it, the need grows to become irresistible; I become possessed by a kind of slowly-exploding rage until I have (by whatever means) created an adequate margin.
All this is exacerbated and enforced by my not having a great deal of energy - I fairly soon tire of anything; even supposed leisure activities like watching TV. I find 'fun' especially exhausting. It seems that I need (or at least want) a lot more unstructured time, and also sleep, than most people.
I cannot justify this - and it would probably be wrong to try. It all sounds like - and no doubt is - self-indulgence.
I can claim that I would not do what I do, unless I was not busy - but them who cares about what I do? And is it any more, or better, than what other much busier (and more socially valuable people) do? No. Not really. Not remotely.
I know that if everyone was like me, there would be no society; humanity would collapse into chaos, and go extinct.
Thank Heavens for busy people! Salt of the earth! - but I am not one of them.
Note: I should clarify that although I am not 'A Mormon' - not a member nor even an attender of the CJCLDS - I believe all the Mormon doctrines and fully support the church and its leadership.