WARNING THIS IS THE LONGEST POST I`V EVER MADE: Cabinetman is right a mortice and tenon should be a sliding fit IE you should not have to beat it to put it together or beat it to take it apart.
You`ve raised a interesting theme with the size of the M+T, so I hope you don't mind if I take a walk through it with you and just say how I would do it and why.
Like most things in wood work there are no hard and fast rules how to do something that's why when you have two wood works you have three different opinions on the best way to do a job.
But there are things called rule of thumb,Most of them go back to the sixteenth century when most things where built on custom and practice and mathematics had not really been introduced into wood work.
In shipbuilding jobs where inspected by the kings man and given the thumbs up or the thumbs down that's where the saying rule of thumb comes from. OK that's the end of the history lesson back to the M+T.
You may think that by making a big tenon you would give it strength and in truth you would but the mortice would have to be cut out big and this would weaken the stock with the mortice in it.
Usually this is where the rule of thirds comes into practice that is one side of the mortice would be 1/3 the width of the stock, the tenon 1/3 and the other side of the mortice would =1/3.
So you say the leg is 5" wide this would give you a tenon of 1 2/3" thick, well that's to wide as you say the apron is 1 1/2"thick so I would make the tenon 1" thick and allow for a shoulder on each side of 1/4" I like to have shoulder on the tenon because when you bring the joint together it strengthens the joint up.
Now the width of the tenon or as you call it the height,now we come into the rule of 1/5s.You say you would make the tenon 3" wide but really this is not wide enough,why? The stresses that are in the apron will try to curve it in the 6" direction, this stress is called cupping so to stop it you need to make the tenon as wide as you can. But the rule of 1/5s says that a tenons width should not be more than 5 times its thickness and the width of the apron is six inches,so what to do.
If you where to cut the full 6" in the mortice the top of the joint would be open and this is what is called a slot mortice and is the wrong joint for the job because it would not stop the apron from cupping.
So material needs to be left at the top of the mortice to hold the joint together. How do we do this? What we do is create what is called a haunch, what is a haunch,its a very short tenon in this case it would be only 1/2" long and coming from the top of the apron extend down 1 1/2" then the true tenon would start and would be
4 1/2" wide. on the bottom of the tenon I would make a 1/4" shoulder so I would have a shoulder right around the joint,so the true tenon would be 4 1/4" wide and within the 1/5s rule.
Now you might say this is all over the top, Ok, but taught is taught
if you now it you can work to it ,if you don't know it, you cant.
So now we come to the depth of the tenon,the longer you can make a tenon the more strength it has but we cannot make the tenons through tenons because one tenon would cut across the other.
The center of the leg is 2 1/2" then half the thickness of the tenon is
1/2" so that is 3", each tenon would be 3" long and each mortice would be 3" deep,the end of each tenon would be mitered so the tenons would meet.Actually the miters are cut short to allow for the glue that will be pushed in to the joint.
Even with the glue I would use a mechanical method for fastening the tenons in place, the method would draw boring, but that's another thing. have fun Billy