Well I had a expansion tank on my Series 1 many years ago and it worked well.  If they are not needed why do modern cars have them - no it is not because the radiators are smaller it is because it is a catch system to catch expelled coolant and return it to the engine when it cools.  The reason radiators in modern systems are smaller is because the systems are more efficient than older systems.
Noting that there are two types - one where the extra tank is not part of the cooling system as such - is basically a catch container for spilled coolant and is outside the pressurised system - this needs a different radiator cap that allows the pressurised system to suck coolant in the extra tank back into the system as it cools and depressurises (my 101 system).  The second as per most modern vehicles where the extra tank is part of the pressurised system and the radiator cap is not on the radiator but on the expansion tank and it acts to just hold extra coolant as pressure in the system goes up and down (like my RRS).  
If I ever get my cars going I will be putting one in where the extra tank captures the coolant and lets it back when the system cools.
				
			 
			
		 
			
				
			
			
				REMLR 243
2007 Range Rover Sport TDV6
1977 FC 101 
1976 Jaguar XJ12C
1973 Haflinger AP700
1971 Jaguar V12 E-Type Series 3 Roadster
1957 Series 1 88"
1957 Series 1 88" Station Wagon
			
			
		 
	
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