LC, if a minhag was completely arbitrary, we would call it it a minhag shtus or taus and disregard it.
As it happens, the A”H’s shittah is based on the shitas Rishonim that the gemara’s din of waiting until the next seuda means the normal time between seudos, so calculating from the end of the seuda makes sense. The gemara’s reasoning would be something like a “lo plug”, which although not seeming to match the din with the reason (which would be true whether the reason was digestion, ta’am, or meat caught between the teeth), is common enough and not arbitrary. It is Chazal’s way of implementing takanos in a way more likely to be followed.