Sufficient accuracy can be obtained from an ARP position entry. Any minute errors in platform alignment you generate will be insignificant, and DME/DME update will give you the correct position and a reference for FMC position. Bear in mind that initial position is used by the platform for coarse alignment and that fine-tuning takes out most platform alignment errors, with runway update (if you have it) taking out any starting pos errors. Only if you are going many miles into non-DME territory do you need to even think about gate position - and then screwing it up.
If you are going to be reliant on extreme position accuracy then use gate position, and you are of course in the wrong aircraft - get a GPS based system
I was once told that at least one major airline, operating in a DME rich environment, did 1 full align first flight and then left it in NAV all day.
Considering most of us normally finish with an ILS or radar there is no real issue. IF your route is over sparsely beaconed territory, you MAY benefit from a gate position - but make sure both of you check the entry. In many cases ARP is not THAT far from gate anyway.