I disagree. After Theodosius, Constantinople itself never faced any serious threats from the west. Even Attila proved no match for the walls (the 'recently rebuilt after an earthquake in a slap-dash effort by a bunch of amateur' walls).
By controlling the bottleneck from the western half of the hellespont, Constantinople (and, to a much lesser degree, the Long Wall of Thrace) was able to block any force in Europe from invading Anatolia. Being on the other side would simply mean that there'd be no major fortifications on the west coast to block their passage (other than the fact that Byzantium would be almost impregnable anyway, instead of 99% impregnable) through into Anatolia.
Greece and Thrace would be just as ravaged as they were historically. Meanwhile, the capital would indeed be more vulnerable to the forces that could actually mount any serious sieges, the Persians and, later, Arabs.
Though, if you're looking for a capital in Anatolia, why not just go with Nicomedia?