Sentence Correction

(a) and (c) are both GRAMMATICALLY correct, but (c) is absurd.

"lobbied for" implies that the stadiums didn't yet exist at the time.

in (c), "had fewer seats" is in the same tense as "lobbied" (i.e., the simple past tense), thereby creating parallelism.
this parallelism implies that the stadiums already existed -- and "had fewer seats" -- at the SAME TIME that MLB was lobbying for them. that doesn't make sense.
if we were to amend (c) in the following way...
lobbied for stadiums that would have fewer seats to reduce supply and increase ticket prices
...then it would also be correct, albeit bulkier and more awkward than (a).

a couple of comments:

in A , WITH is unclear

nope. totally clear.
"X with Y" is a perfectly acceptable method of expressing the idea that X has/possesses/owns/exhibits Y.
e.g.
women with red hair
stadiums with fewer seats
heterosexuals with AIDS
etc.
these are all viable.

--

But C has a issue. Usage of past perfect tense..."had fewer seats" is not suitable

that is not the past perfect.

that's the normal past tense.
"had" is the past tense of "to have".
in the past perfect, this would actually be "had had".

see here:
https://www.beatthegmat.com/though-he-ha ... tml#184296