Not sure what you mean by display full folders - if there are thousands of search results, it is not practical to load all these at once for the end user to view. Only a screen's worth of image thumbnails should be displayed - i.e. use a paging mechanism. If the user scrolls down, load the next set of results.
If you mean the search results themselves don't return, this depends on what API call you are using:
"searchAssets returns up to 1000 assets in a single call. To return up to 10,000 assets per call, limit the response data to a subset of the totalRows, name, handle, type, and subType fields. To return larger sets, set up paging with the resultPage parameter. "
There is also getAssetsByName and SearchsAssetsByMetadata.