Thinner PCB might be actually more favorable from signal integrity and EMC perspective, if one must work with two layers only.
That makes it possible to make thinner traces over ground plane (microstrips) to get decent impedance. Also, stray fields from traces come down as the distance between ground plane under the trace and trace itself becomes smaller. As a rule of thumb, trace width equal to dielectric thickness corresponds about 75 ohms microstrip trace and twice the trace thickness to the dielectric thickness is about 50 ohms. From that, it is easy to see that it is quite difficult to achieve reasonable impedance on 1.6 mm boards (or, 0.8 mm for that matter). You just can't fit the traces in, unless you are working with RF, where signal count is usually low.
For typical 4-layer buildup, the dielectric thickness between ground plane and signal (layers 1-2 or 3-4) is in the order of 0.2 mm, and it is easy to do those 75 ohm traces. 50 ohm ones are still quite thick.
In some cases, it might be necessary to make thicker PCB's just because your impedance would drop too low for reasonable trace widths in inner layers (striplines) otherwise. This becomes an issue when you have something like 16 layers (of which about half are power and ground planes).
Regards,
Janne