I believe you mean the parkways have limited clearance, especially the Southern (State) Parkway which along with the Meadowbrook, Wantagh, Robert Moses Causeway, etc. parkways serve the South Shore beaches as well as a number of state parks (e.g. Hecksher). The Northern State does as well, but North Shore LI beaches are kinda meh to begin with).
The LIE was designed to handle commercial truck traffic (and was build on Long Island starting in the 1950s), so it was build with sufficient clearance in mind. But again, the limited clearance on the parkways to the beaches pretty much ensure you need to get off the LIE, and take the slower arterials (South of Sunrise Highway there are no clearance issues to, say, Jones beach, which is how buses get down there nowadays).
Still, more convoluted that taking the Southern directly to the Wantagh Parkway south*.
*But not necessarily faster or easier - in fact I often need to take the arterials when the Southern (and Northern and LIE as well) get jammed packed sometime after 3:00PM on a Sunday with good weather.