Eggbeaters are easy to clip in to, but you need the sole-savers to protect your shoes – then you can’t clip in nearly as easily.
I had a couple of pairs, as did MrsF. This happened to both of us, and happens to most eggbeater-users eventually. It can be fixed, but it’s bloody annoying when it’s 15 miles from home on the first day of your holiday.
My cleats lasted very little time, 3 or 4 months a set.
If the bottom of the pedal hits anything, the top of the pedal opens releasing your cleat.
Shimano SPDs are better in every respect apart from weight. Reliable, easy in, adjustable spring tension, long-lasting, cheap too. The problem with your cleats coming out on max tension is probably that your cleats are worn out or they’re not aligned properly.