Some languages do have very free syntax even without case marking (and with very weak other strategies of disambiguating) - a language can rely fairly well on things like the meaning of a verb (a clause along the line of 'a taxman stole the bike' is quite unlikely to, in any serious setting, have the bike stealing the taxman - and many languages simply just use this knowledge.)
Cases don't really offer much different from what adpositions offer, except maybe the option of introducing congruence (but e.g. many Russian verbs with prefixes have something along the lines of adpositional congruence with the verb). Congruence of course increases the amount of redundance, which is useful. (Or else languages probably wouldn't have systematic ways of encoding redundant bits of information every here and there). Most Biblical Hebrew prepositions don't differ much from case, in that they affix to the noun.
Cases likewise lack the option of using a case marker intransitively (unless you use some kind of dummy pronoun or whatever to carry intransitive case). Of course, not all grammarians recognize the term "intransitive adposition", but I think the term makes sense. Read
http://www.abc.net.au/radionational/pro ... on/3521076 - although one can disagree on whether what he found properly is an intransitive adposition (or something more like an omitted adposition), the idea of calling adpositions without explicit objects intransitive makes a great deal of sense. Such do lend the language a new dimension of reuse.
Some languages permit coordination of adpositions:
around and beyond X
with or without Y
This is not permitted, normally, with cases, although I bet some language that normally is described as having cases has come up with a clever way around that (maybe something like house.at and.in?, house.at dummypronoun.in, whatever)
Many languages permit coordination where different surface cases are demanded, e.g. some languages that have verbs that require objects in other cases than accusative can permit two verbs that require different cases from each other to take one common object according to some resolution strategy. (same goes for adpositions that govern some case.)
In the case of adpositions and verbs governing some case, this does increase the redundance a bit - if there's ten verbs that demand an object in the allative, and you hear an object in the allative - but you only hear half the verb, it's likely your mind can puzzle together what was said without you ever knowing your mind in fact did exactly that. OTOH, adpositions and other things may also contribute to such redundance. (same redundance thing goes with prepositions - if all prepositions denoting direction use accusative and all denoting location use locative, and you miss the preposition but hear the case, you got pretty much of the message already!)
Of course, adpositions or verbs governing cases is a kind of congruence as well, although less obviously than e.g. nouns and their adjectives taking the same case.
So what can we do with case or adpositions? We can encode information about participants in a verb phrase - does the subject act of its own volition, is the object wholly affected, is the object/subject definite, what kinds of participants are there (here, English kind of has syntactic case - subject, indirect object and direct object; other languages slice this up differently, some entirely even merging direct and indirect objects, some having the transitive subject distinct from a merged intransitive subject and transitive object.)
Differential object marking is quite a common phenomenon (wikipedia says 300+ languages)- e.g. Finnish, Turkish, Spanish, Biblical Hebrew and Malayalam have it. Here, case marking tells us something salient - in Finnish, it gives away the telicity of the verb, in Turkish and Hebrew the definiteness of the object, in Spanish it gives away that the object is specific and human. Of course, in the case of Spanish, this is accomplished with a preposition. This also is the case in Hebrew (and one that actually doesn't merge as often as, say, b
e- or l
e-).