You're talking as if the Phantom is unrivalled. There is nothing about the Phantom that the Mulsanne or Arnage doesn't have besides bulkiness.
It's not about bulkiness. It's about the cabin atmosphere & layout & design - which in eg. Bentley & Maybach & even in Ghost is more typical car like.
While the sensation in Phantom's cabin is beyond car. You sit much higher, having a command almost SUV-like driving & sitting position, even more so in the back - where you sit above the driver level. the interior layout & design (front) looks & feels like a yacht, while in the back seats it's like a lounge.
I'm sure car-wise Mulsanne is better than Phantom - it's also newer ... so that's expected. And I'm sure VAG put all the finniest & latest tech in the car.
But presence & prestige wise ... yes, Phantom is still, and will be unchallenged. Only Bugatti has a potential to surpass Phantom in exclusiveness & prestige. And I'm sure VAG will do it.
So the positioning between Bentley-RR-Bugatti will be like this:
Continental > Ghost > Mulsanne > Phantom > Bugatti uber-sedan
PS. BMW elements are well visible in the Ghost
Yes, the proportions & layouts are similar - since the platform is same. But visible STYLING elements are not present at all.
Name one.
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Regarding Mulsanne ... I must admit I like Continental series better ... since that was really a fresh approach to the Bentley design - modern yet typical Bentley: nothing radical but appealing.
While Mulsanne looks like an old lady with a facelift.

Or like HRH with tons of botox under the skin of her face.
But ... I'm sure there won't be much cross-shopping between Phantom & Mulsanne - the clientèle is different.
But ... I can see many potential Mulsanne buyers (who buy a driver's car in this segment) checking will look down to AM Rapide & RR Ghost. Not as expensive, but I'm sure almost as prestigious.
C'mon ... look at the Ghost interior pics & compare them to Mulsanne interior. Even Ghost interior is more exclusive & prestigious looking than this one from Mulsanne. I'm sure the materials & fit+finish will be superb. But the design & layout aren't anything special at all. Not being exclusive & excuisite enough. And that's what it counts in this segment.
Why do you think Maybach is a fail. Although it's a superb car ... ITS DESIGN IS NOT SPECIAL, DISTINCTIVE & EXCLUSIVE ENOUGH!
Sure Mulsanne is a fine car but I'm 110% sure it won't dethrone the Phantom. Will it be commercially successful - of course it will. But image wise stil inferior to Phantom. Ask any automotive guru if you don't believe me.