R. Leibowitz’s view of the Kotel as Avodah Zarah rings so true here. However, everyone, both Chareidim, Dati Le’umi, Chilonim and Reform have a right to worship Avoda Zara in the modern State of Israel. After all, Chacham Ovadia writes that it the State of Israel has to protect churches under its domain, and he holds like the Rambam that they are places of Avoda Zara.
That being said, I have long pushed for those who want to daven differently than the norm to free up Robninson’s Arch: there is no reason it has to take second fiddle to the “Kotel”. It is still the Western Wall and has more interesting Roman-era artifacts. It needs to get security and be open 24/7 like the Kotel and just leave the Kotel – for now – to the chareidim and the shnerrers who bother you when you try to daven there. Start putting kapitlach in the Southwestern Kotel! The Israeli Supreme Court has said that any kind of Jewish worship is permissible there, so those of us who want to try non-normative, and even more pleasant, services should concentrate on consolidating and building up Robinson’s arch, and then, if necessary, move on to the Kotel.