I agree that 1500 is arbitrary 
The fact that 1500 corresponds to 6 kyu basically says that if everyone is given the same starting point of 1500 and Glicko is allowed to do it’s thing, then the players that end up with this arbitrary rating of 1500 are those of a strength of approximately 6 kyu in other systems (AGA, EGF, etc.), as determined by surveying members for anchor points. Therefore, we will call this arbitrary rating of 1500 by a certain rank to give it real world meaning and that happens to be 6 kyu. Choosing a different starting value like 1000 or 500 will just change the conversion between internal rating and external rank, e.g. 1000 = 6 kyu or 500 = 6 kyu. So, yeah, that would be pointless. 
But I’m not saying to change the starting value of all players by the same amount to some new default like 1000 or 500. I’m saying, now that the system is established with some anchoring to other systems, new accounts can join at the approximately correct level if known (i.e. rank from another system if known or 30 kyu for raw beginners) so new accounts will join at a variety of levels that are closer to where they are likely to end up under the current system of starting them at the likely incorrect value of 6 kyu. Deviation and volatility would still be unknown so just use the default values.
Looking at the Glicko equations, this will work fine. If anything, it will improve stability. Essentially, the Glicko equations mean that:
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Playing stronger opponents has more potential to increase your rating than playing weaker opponents (step 3, definition of E ~ 1 / (1 + exp(mu_j)) where mu_j is opponent rating). The size of this effect is relative to your current rating (the above is actually E ~ 1 / (1 + exp(-(mu - mu_j))) where mu is player rating). Therefore, having an incorrect initial rating means you will adjust faster. With an approximately correct initial rating, you are already in about the right place so there’s less adjustment to do anyway.
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Opponents with a high deviation are weighted less favourably than opponents with a low deviation (step 3, definition of g ~ 1 / sqrt(1 + phi^2) where phi is deviation). Therefore, provisional accounts (high deviation) do not affect their opponents’ ratings as much as games with established players. Hence, the impact of incorrect initial rating is relatively small on the opponents’ ratings compared to, say, sandbaggers with non-provisional rank who decrease their rank on purpose. However, allowing declared rank and thus approximately correct initial rank would reduce the effect on the rank of the provisional player’s opponents even more. So, in effect, there is an extra element of rating system instability by having usually incorrect initial rating that would be eliminated by having declared initial rank and thus approximately correct initial rating.
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Winning will increase your rating while losing will decrease your rating (step 4, definition of Delta). Again, results against opponents with a high deviation are weighted less favourably. This aspect of the equations doesn’t make too much different to the current discussion. The important points are the two above.
So, actually, when you consider the above, declared rank is better for new accounts (especially beginners) and better for established accounts as well (both due to better matchmaking) and it’s also better for the rating system stability. So, there is no reason not to (apart from time and effort to implement) and lots of positive reasons to do it. 