Foot over bridge!

This term is being used by almost all and sundry in Bangladesh, which is neither correct grammatically nor as a compound word.  The word 'over' comes into use as an alternative to the word 'across'. For example: "We went across (or over) the bridge, to reach the restaurant." From the word 'foot', many terms have come into English language, like: 'footing', 'foothold', 'foothill', 'footlights', 'footslogging' and many other words that can be found in the dictionary.
The term 'foot over bridge'; is neither here nor there and over and above it is not grammatically correct too! Would it not be better to call it: 'pedestrian bridge'; which is closely related to the word pedestrian crossing and is also functionally speaking more appropriate and correct? For the use of elderly or physically hampered people there is a lift on both ends both for going up and coming down the pedestrian bridge as I have seen in many developed countries.
I would invite comments from readers and teachers in English grammar and composition, for their valued comments on this matter. I have been curious about the correct usage of this 'term' for many years wherever the elevated pedestrian crossing is needed to be written.
Engr. S.A.Mansoor
Dhaka.