Nonsense. People clearly do remember these things. People still bang on about the European referendum of 1975 in Britain, and that was over four decades ago. Referendums invite a national debate in a way that absolutely nothing else does. Do you think that the Scottish independence debate is going to be forgotten any time soon? Of course not. They can have huge impacts on the national psyche - and that impact is an incredible impact to make when it says "we, as a community, embrace LGBT people". You don't get that from a court ruling.
I also disagree it's the easiest way. If this were true, then it should also be true that countries with strong judicial systems have embraced gay marriage before those with weak judicial systems. This is not true, and if anything is the *opposite* of true. Australia, the United States and Ireland all have, amongst English speaking countries, relatively strong judicial systems - particularly the United States. As it stands, the odds are very reasonable that the United States will be the last to have nation-wide gay marriage, or at the best very slightly before Australia. Meanwhile, the United Kingdom, where judicial powers are relatively non-existant, passed a gay marriage bill under the aegis of a socially conservative government. The reason, or at least one of the reasons, was that the LGBT movement never tried going through the courts and was a *lot* more active at having conversations with the public at large. The pattern is even stronger when we expand past English-speaking countries. Belgium, the Netherlands, Spain, Canada - none of these countries have histories of strong judicial oversight.
It may be the cheapest way, sure. But given that a) it's probably the slowest way, and b) the actual effect it has on integrating the LGBT community into society at large is so much smaller, I just can't stand by relying on the courts.