For a PCB that will be tested on a bed-of-nails test fixture, placing test pads on only the bottom side of the board is the single most effective thing the designer can do to reduce the cost and complexity of the fixture.

Double-sided fixtures don't just double the task, they are significantly more complicated.

Single-sided fixtures can get away with simple mechanical arrangements to locate the board and press it down onto the test probes. Locating can be achieved with spring-loaded pins aligning with tooling holes. A simple hinged pressure plate can be used to close the fixture and press the board down on to the probes. Alignment of the board with the probes is automatic since probes and alignment pins exist together only on the bottom side probe plate. Relative alignment of the top side pressure plate is not critical.

By contrast, a fixture with probes on both sides typically requires a parallel-motion closing mechanism, since probes must land accurately on both top and bottom sides with no sliding motion. This usually requires linear rods or rails, linear bearings, and a cam-operated mechanism. The fixture must be significantly more solid and robust, to keep top and bottom probes aligned with each other and the board.

Double-sided fixtures can also be less convenient to use, since there is often less access and clearance for placing and removing boards than in single sided fixtures where the pressure plate can hinge well away from the board.

Strongly prefer single-sided probing if at all possible to make your boards more easily testable.