1) As productive capital becomes increasingly digital, it becomes cheaper to acquire or create. If capital is cheaper to acquire or create, it means fewer people are needed to pool money to attain it. In other words, capital ownership becomes more concentrated as a result.
2) Additionally, digital capital often enables production at near 0 marginal cost (e.g. it costs facebook virtually nothing when a person registers a new account). Markets where the marginal cost of production is near 0 are generally 'winner-takes-all' markets (e.g. natural monopolies, network monopolies etc.), due to always increasing economies of scale. So the returns to capital become larger, as monopolists can capture more 'consumer surplus' as profit. In addition, the more a monopolist can price discriminate (i.e. set different prices for different consumers, based on how much those consumers value the product), the more they can convert consumer surplus into profit for themselves.
The net result of the previous two points: significantly more wealth becomes concentrated in fewer hands
3) Digital capital is highly mobile. For example, AWS instances can be moved to another country almost instantaneously and without cost. This makes it hard for governments to tax returns to digital capital, barring some global tax agreement, as raising the tax rate on capital returns will simply cause it to relocate to lower taxing jurisdictions (e.g. Ireland). So governments have limited scope to redistribute this increasingly concentrated wealth using taxation.
I think that we badly need to have a global conversation about this: do we consider these good or bad things? are we ok with the resulting society? what should we do (if anything) about this?
I see how that would cause ownership of a specific asset (e.g., one program) to become more concentrated, but wouldn't the lower barrier to entry cause ownership to become less concentrated market-wide?
1) We don't care about wealth distribution per se. What we actually care about is utility maximisation (in other words, maximising the sum of 'human happiness').
2) Once we get pass some basic wealth level, to meet some set of basic needs like food and shelter, a person's utility is a function of relative wealth rather than an increasing function of absolute wealth.
3) If you accept points 1 and 2, we therefore should care about wealth inequality in and of itself.
There's also probably another argument to be made along the lines of 'decreasing marginal utility with respect to wealth'. Which is a fancy way of saying: a poor person derives greater utility from an additional $1 in wealth than a rich person does. This would mean that the sum of human utility is increased by taking $1 from the richest person and giving it to the poorest person.