1. Algorithm designers collects all the data. At present they have (almost) perfect data as they get actual transactional prices from their customers. This alone gives them huge information advantage against renters. With public information you generally only see offer prices and how long the place is listed (often even with some missing location details)
2. Algorithm ensures consistent interpretation of data and factors that affect pricing. When its human interpreting data you will have inconsistencies, eg how far does some undesirable neighbour location affects prices, how long does listing remaining available is a problem, do you think that transactional price matched the offer etc.
3. The sad truth is that this whole thing is about making market less efficient in raising housing prices. Given terrible under supply and importance of the housing need for people even simple, stupid algorithms like "match neighbouring landlords plus a bit" will lead to price increases. Its just that automatic systems remove fear about taking bad risk and allow for more aggressive strategies.