I paid £8.94 for the base game and both expansions during the Steam Autumn sale last year. Personally, I would not recommend paying full price for the expansions as I have found they add little to the experience and come with their own set of gamey exploits and quirks.
Nonsense. For instance AHD brought the whole game to playable speed (multithreading support). Before that it was immensely painful to organize naval stacks due to lag and the global unit spam bogged the game speed down. By 1900s it was terrible. It was very unappealing to even consider to continue to the finish line.
The only thing that's rather useless by now is the alternate starting bookmark (American Civil War). Perhaps someone uses it, for me it's completely useless.
Important mechanisms not in vanilla:
*Creating a casus belli (AHD)
*Popular movements and their suppression (AHD)
*Civilizing a country not on-off decision but there are paths including multiple different reforms (AHD) - ok, it has its flaws too, like RP through conquest but anyway
*Crisis mechanisms (HOD)
*New colonization system (HOD)
*New naval combat system (HOD)
*Changes to land combat (HOD) - major rebalancing of the units
Quality of life:
*Funding your capitalist's projects (AHD) - imagine how long it takes if you start with 0 capis and you need to create enough wealth for the new capitalist class to be able to build even one factory... might not be done in a decade. So if you wouldn't be state cap... RIP quick industrialization
*SoI management easier by introducing going past max influence, which deducts from your competitors ability to gain influence (AHD)