Really? I had heard that the horse collar was a great boon to peasant farmers, since before its introduction they had to rely on generally more expensive and slower oxen for plowing and the like. The introduction of the horse collar to peasant farmers, then, was kind of like the early 20th-century introduction of faster and cheaper internal combustion tractors that would replace the slower and more cumbersome steam tractors.
The horse collar, then, would allow peasants much greater agriculture production, resulting in surplus goods, greater incomes for the rural lower class, and greater impetus for trade.
The history of technology is in what, among professional historians, is generally referred to as a state of being a fucking mess.
Seriously.
It was all much easier in the fifties and sixties when everybody knew that a later technology had to be superior by virtue of replacing the older one. If this replacement coincided - or appeared to coincide - with a major change in the tide of history, then clearly it must have been a decisive factor (see stirrups and the Huns). If you've lived through the industrial revolution's tail end, it is a pretty intuitive idea, but unfortunately it doesn't actually seem to be like that.
The horsecollar assumption suffers from the fact that we still don't really know what the ancient harness actually was like. We have reasonable approximations, but from the extant data points you can build both something that will kill your horse and something not much inferior to a collar.
Recently, it has been theorised that the adoption of horses over oxen for traction had nothing whatsoever to do with the collar - its introduction is coincidental, but unrelated - and was instead motiovated by increased productivity of grain farming. Horses are more focused, faster, more biddable and more flexible than oxen, all of which makes them the favoured choice, but they eat grain, so a certain productivity was required before using them for agricultural labour paid off.
Horses in medieval Europe also replaced mules and donkeys in a lot of roles. Parse that with a Whig model...
I am firmly convinced stirrups are overrated (I have seen an armoured rider on a Camarque horse saddled Roman-style execute a couched lance attack on an 80-kg sack on a mock horse and unseat it - usual caveats about reconstruction apply, see abover - no, we don't really know how a Roman saddle was constructed).
I am also not sold that widespread watermills were a medieval innovation.
I do not buy the explanation that slavery stifled innovation because it would seem to apply only to the Romans (it's not like the hellenistic world did not practice slavery, and medieval Europe's most progressive areas were also those where chattel slavery was most common).
But that's neither here nor there. All of these things would be interesting for the Romans. Yoghurt I suspect they had - at least, that is what 'melca' appears to be. And lactosae intolerance is not a big deal among the Mediterranean population today, so I doubt it was then. In evolutionary terms, 2000 years is nothing.
What I would think A really interesting innovation for Rome to have would be proper statistics. We have some surviving economic documentsw and administrative files, but they are often fairly unsophisticated. I am not sure whether remedying this would require Indian nbumerals or not - I rather suspect not, given how much yopu can do with an abacus and geometric solutions - but it would require a sophisticated understanding of the universe of numbers. A Roman world that understands things like tax return curves, investment returns, opportunity costs, statistically relevance, confidence intervals, risk premium calculation and such could be a genuinely frightening prospect.