The RM & USMC both started out as soldiers on ships for fighting in naval battles, which were then conducted at ranges, & in a manner, in which men with muskets & bayonets could be useful. Both also had secondary roles as on-board security, & for raiding ashore. When the nature of naval warfare changed, marines in many countries ended up being divided into base guards (little more than police) & raiders, & greatly reduced in numbers. Some managed to find new roles, e.g. the USMC became a colonial army, delivered by the navy to whatever small country the USA wanted to occupy.
Amphibious assault was never exclusively or even primarily a marine task. If you're in a war which necessitates sea-borne invasions, you need to use your army, not just the marines, as WW2 proved. The USMC reinvented itself as the amphibious assault force of the USA post-WW2 to keep its manpower & budget. It's not an ancient tradition.
The RM, USMC, & every other 'marine' force larger than a small raiding unit consists of ground troops, & whenever their nations are in a war they fight on land. How many US marines are there in (landlocked, not even a navigable river) Afghanistan?
I think there are ~20,000-25,000 US Marines currently deployed to Afghanistan.
I think the USMC is headed for something of an existential crisis. With the cancellation of the EFV, the F-35B on the rocks, an increasingly broke US government looking to cut costs, and the fact that the US has not launched a major opposed amphibious assault since Inchon 1950, I suspect the USMC is going to start looking like a redundancy to some folks in Washington.
I think it's questionable if an opposed amphibious assaults against a reasonably serious opponent is even possible today given the advances in SAM, ASM, ATGM, sea mine, and submarine technology. Unless of course the USN and USAF bomb the opponent into oblivion, and then its not really an opposed landing at that point anymore, is it?
I don't think the USMC is going to disappear, but I wouldn't be surprised at all if it ends up a lot smaller.
I think the niche the USMC will ultimately fill will be something akin to a seaborne version of the US Army's Ranger Battalions - a highly trained, highly mobile, spec ops capable light infantry force, configured for small unit (battalion sized and under) operations, as well as providing security teams and boarding parties for the USN.
Which isn't all that different than what they do now - just on a smaller scale.