How to extract a specific element from EXIF photographic metadata?

Does this do want you want?

Cases[Options[i, MetaInformation], 
 HoldPattern["ExposureTime" -> ___], Infinity]

or even simpler because it is Rules all the way down:

Cases[Options[i], HoldPattern["ExposureTime" -> ___], Infinity]

{"ExposureTime" -> 1/65}

All-in-one:

With[{wanted = "ExposureTime"}, 
  wanted /. Cases[Options[i], HoldPattern[wanted -> ___], Infinity]] //
  N

Here is something based on FilterRules and using your post of Exif metadata format.

FilterRules

FilterRules["Exif" /. (MetaInformation /. Options[i, MetaInformation]), "XResolution"]

{"XResolution" -> 300}

There may be more elegant ways to extract the rules which form part of MetaInformation, I await them with interest.

This unpacks nested sets of rules:

FilterRules[ Options[i, MetaInformation] //. {_ -> z_} -> z, "XResolution"]

{"XResolution" -> 300}

OptionValue

Here is an interesting alternative which does require some knowledge of the structure of the MetaInformation but is otherwise nicely concise.

OptionValue[Options[i, MetaInformation], MetaInformation -> "Exif" -> "XResolution"]

300

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