I think that the RAF Hawk accident was due to the ailerons not being connected at all. Subsequently they introduced a procedure whereby the starter crew indicated control deflections to the pilot during the after start control checks.
One problem related to cockpit control checks is that some control surfaces are not visible from the cockpit, especially elevator and rudder trim tabs. The only way that you can then check these is during the pre-flight walkround having set full trim deflection first. However, this requires careful thought because the tab will deflect in the opposite direction to a control surface and will require you to go back to the cockpit to then set the opposite direction. Also, if an aircraft has a mechanically linked nosewheel steering system then full rudder checks can only be performed whilst taxiing and that is not the time to look over your shoulder at the rudder, which possibly you cannot see anyhow. So, there are a few practicalities which do require robust engineering procedures and pilot observations cannot always be used as a mitigation.
There is one interesting control reversal issue that does occur and that is for a pilot from a three-axis control aircraft flying a weighshift microlight (and vice versa). The pedals will generate a yaw rate in the opposite direction for each of these classes. Whilst low gain tasks such as taxiing can be performed with conscious decisions, correction of an uncommanded yaw disturbance during take-off and landing can result in the pilot making an unconscious skill-based pedal input in the wrong direction.