I heard an aviation expert state that a transatlantic liner would not be able to make it across the Atlantic unless it could fly at the designed altitude.
In addition it was stated that the skies would become dangerously over crowded if all aircraft were to fly at the lower altitudes as more would be squeezed in to a smaller air space.
Exactly. Passenger aircraft rely on flying in very thin air to get their range and performance. Whilst there might be a little flexibility in altitude, to suggest that an airliner could do a transatlantic flight without going over 20k feet (for example) is like suggesting that you could drive an Omega from London to Edinburgh on a tank of fuel - in 1st gear.
Outside what the aircraft is technically capable of, you have to consider what is economically viable for the operator, as well.
Over and above that, you have to consider the extra workload and crowding of the airspace involved in taking aircraft outside the usual operating regimes to "fly around / under / over" this ash - assuming you know where it is.
As I said before, we are talking about a system with very little "give" when it's working properly. Throw in a few, seemingly minor, complications and it grinds to a halt.
Kevin