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Thanks Bobbo. Your thoughts are greatly values.
The plan is for a mid size dining table, but I’m more concerned with rigidity than strength, but wood dowels in a shallow hole is probably not good in either. I guess I’ll have to do a mock up to test.
Maybe a metal dowel through the face would be better. Small polished stainless circles might be a nice feature. But then again if I use stainless screws and polish the heads it might look just as good and could be disassembled. I think four to five dowels or screws for each leg...
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I’m more concerned with rigidity than strength
The structure will be pretty rigid. The problem as I see it is the joints pulling apart over time with the day to day movement and use of a dining table. The drawing above will be pretty strong especially if you use some kind of epoxy glue to hold it all together. I'd be tempted to put some kind of metal bracket at the top and bottom of the leg for a bit of extra strength.
It all comes down to how long the table legs are going to be. I can't see those legs being strong enough for anything much taller than a coffee table.
The strongest way of doing it without mechanical fixings would be to make the dowels narrower on the ends than the middle, this will give you a bigger surface area for the glue to hold. Looking at your drawing I'd turn the dowels on a lathe so that in the middle you have a 15mm long by 13mm dia section, then at either end you have a 10mm long by 10mm dia section. The end sections can then glued into a corresponding hole in the leg sections, making sure that there is good contact for the glue between the face of the leg sections and the step in the dowel.
Alternatively you could countersink a screw into the face of the wood and plug it.