There is no question whatsoever about whether you should have charts on board. You MUST. I support other comments also that you shouldn't rely on electronic solutions solely. You also need to know how to use the charts properly, how to interpret the depths related to the tide height from time to time etc.
As the operator of a vessel, you have certain obligations to avoid collisions, operate in a safe manner etc etc; if you don't know where you are in relation to any submerged hazard or channel marker or any other relevant feature, then you are not operating in a safe manner; obligations aside, you owe it to yourself to keep 'you and yours' safe. Is it acceptable to cruise into a prestine bay and drop anchor when you feel the boat skim the bottom? I think not.
Most of my sailing for now is day sailing out of the marina on a large bay (Western Port), keeping usually within 10nm of the Marina. I have a chart of the bay at hand at all times, and I always have a line on the chart to guide me; I take fixes (with GPS and with hand compass from time to time to keep my hand in) to confirm my proximity to the charted course.
Before the day out I prepare a sheet that I take with me that has: Boating weather, sunrise and sunset times, tide highs and lows for the day including a graph of tide heights by time (using the twelfths rule), and considered commentary about direction of current and any other factor that may influence my day out. It's a lot easier to think through your 'plan' in the comfort of home before your trip, rather than trying to read and interpret later 'at sea' when it's all going wrong for any other reason.
There are just too many risks associated with operating a vessel in close proximity to the shoreline that can be mitigated by a responsible attitude to simple navigation disciplines.
Besides, if you run aground, it can ruin your day!
(No worries mate!)
Western Port Marina
Hastings, Vic, Australia