The problem with two separate transformers with their primary windings in series is considered best under no-load or light-load conditions on the secondaries. What would guarantee that the primary voltage seen on one transformer would be the same as the primary voltage seen on the other?
With light-loading conditions, the dominant current flowing through a transformer’s primary winding is the magnetisation current or, put another way, current due to the primary inductance and its reactance. The magnetisation inductance is not so well defined; one transformer might be 10 henries while another (from the same production line) might be 20 henries. This would lead to big difference in the primary voltages under light load conditions.
For instance, with the inductance difference as above, one transformer primary would receive two thirds of the overall applied voltage. This means that it’s secondary would produce a voltage that is twice the voltage compared to the other transformer’s secondary.
Under full load conditions, the dominant primary-referred impedance is that of the secondary load so, with similar loads, the two secondary voltages would tend to be more equal but, what if the loadings were grossly different? You would have significantly different secondary voltages unfortunately.
Would this happen with a centre tapped secondary? No, because the magnetisation flux in the core is common to both split halves of the secondary and, because of Faraday we know that voltage is proportional to the number of turns hence, either side of the centre tap, the voltages are much more equal even with big loading asymmetries.
Putting the primaries in parallel is a big step to making things more similar.