Sailing here in the Chesapeake, we ran aground several times with our first boat, a Seafarer 30, drawing 4'11" (makes 5 feet look sick!), which is really easy to do with shoaling so common, and no chartplotter on that boat. Two groundings, Selby Bay and Shaw bay area, were due to our inexperience at "reading the water" and how shoaling typically extends from the points of land in narrow creeks; two, around Knapps Narrows, were just due to the fact that the Narrows is not charted accurately, and we needed local knowledge... which we now have! We have unlimited towing from Towboat US, which I highly recommend for the Chesapeake. They are great and it is well worth it. Our soft muddy bottom means no damage, usually, except to your pride.
With our current boat, a Caliber 35 LRC, draft 4'6" and a great chartplotter, (and more experience!) we kissed the bottom once around Knapps Narrows, but immediately got off, no big deal.
We love exploring and gunkholing, which is going to involve some chance for grounding, sooner or later. Even in the Chesapeake, with a small tidal variation, it is best to time being in a shallow passage or entrance to a creek for around high tide... that 6 inches or so can make all the difference!