In a pre industrial society, children are assets.
The reasons why children were assets in pre-industrial societies included not just the love of children (which people still possess, clearly), but two rather clearly economic characteristics of pre-industrial societies:
First, people got their living from agriculture without machines and even small children provided labour for that kind of work. Today children are not allowed to work under those terms and most jobs require education. So the purely economic motivation to have lots of children is not the same today. Because children now need more education they are also more expensive to bring up than was the case in the past. In other words, today's parents can't easily afford large families, because children do not contribute to the family's earnings.
Second, when there was no old age security via governments, children, especially sons in patrilinear societies, were the parents' plan for their own retirement. Given high childhood mortality rates women had to give birth to many more children than today, just to guarantee that some would grow into adulthood.
I don't think the society can be turned into that direction very easily, and probably not at all, absent some giant catastrophe which would wipe out most technological advances.
I have ordered her book so I have not read it yet, but I have concerns about the problems in bringing something back which has clear inherent problems for women (such as unequal status and hierarchical ranking of sex roles in value), unless the problems which caused those are addressed. Women in the West did reject the earlier reincarnations of that system because it tended to favour male interests over female ones.
There are alternative visions for a better world which we could compare to Harrington's ideas. I would begin by looking at all the different countries, what has worked where and why, and I would not just assume that we can't alter the way labour markets work or the involvement of fathers at home etc. For example, we could strengthen part-time work, job-sharing, give incentives to men to take more time off, figure a better way of valuing unpaid labour, subsidise young families with children more and so on.