Really? You ask. Yes, I reply. Why?, you ask? Draw up a chair, I say, and read on...
As the 2000 book The Films Of Steven Spielberg notes, Doom and Crusade don't so much fit alongside Raiders as remake it: in each, Indy is minding his own business until he's told about a mystical object he doesn't really believe in, but he goes looking for it anyway, finds it, learns some humility, and lets it go. (So far, this describes Skull, too.) Apart from the missing gun gag in Doom and the vague reference to the Ark in Crusade, only Skull demands to occupy the same Dr. Jones' life. And it's not hard to see why: a pious, believing Indy is no fun at all; we want him to be a lovable rogue, and share in his excitement when he begins to realize that bedtime stories are real. So whenever he gets chastened and humble, it's time to end the movie and restart his journey on the next one.
The Mummy, on the other hand, tells its own story of how Evy learned to break out of her meek shell and inspired Rick to clean himself up and look beyond his own narrow interests for a change. Oh, and there's the whole Terminator-Mummy thing. Say what you like about the movie, it's definitely not a narrative or thematic retread of Raiders.
Rachel Weisz is a better actress than any of the Indy girls, and certainly gives a more radiant performance, with the debatable exception of Raiders' (but not Skull's) Karen Allen. (Plus, she's English!) And, in a sly way, she's really The Mummy's main character: she rescues Rick from hanging, she prompts the journey to Hamunaptra, she wakes finds and Imhotep up and then takes away his immortality. If you're immune to the charms of Weisz's performance... I really can't help you.
No nuked fridge. No sledding down a mountain on an inflatable raft that magically avoids all trees. No day trip that starts off in the desert and transitions to forested mountains later that afternoon. But you do get fun stunts, a great car chase and soldier mummies. One can argue that individual sequences in the Indy sequels supass those of The Mummy, but the latter's action has more consistency.
Let's face it: Raiders used both of Indy's greatest villains. You have the amoral but not quite evil learned counterpart (Belloq), and a-not-as-smart but definitely evil and creepy Nazi (Toht). How do you follow those up? With a dude wearing an antler hat, a selfish double-crossing rich guy, a hot blonde and Cate Blanchett in a wig and a gym track suit: these were decent characters, but none were really frightening or memorable. Imhotep, however, is a badass with soul, played with understated cocky humor by Arnold Vosloo. He's simply a more compelling antagonist than any Indy villain outside of Raiders.
I won't try arguing that Brendan Fraser is cooler than Harrison Ford, because he isn't - even if he is a good deal taller! But while he doesn't get any scenes as touching or heartfelt as the Crusade blimp discussion or rip any hearts out, he does have a fun, dramatic arc from total screwup to formidable rescuer of damsels in distress. And while O'Connell isn't cooler than Indy, either, his childish goofiness perfectly fits with and accentuates the movie's irreverent, unabashedly contemporary fourth-wall-nudging tone, whereas Indy's sequels have either been overly gruesome and slapstick (Temple), overly slapstick (Skull) or pretty close to Raiders but with an abundance of awkwardly silly lines/sight gags (Crusade).
The Dearth of Lameness
Short Round and Willie. A mine cart chase that plays out like a Donkey Kong game. A scholar whose spent decades researching the Holy Grail, but can't remember three ridiculously simple trap-related clues. A centuries-old knight who speaks elegant BBC English, and has apparently just been kicking back and reading a book for several hundred years. A KGB agent who actually attempts a Jedi Mind Trick. Tarzan Mutt. Etc. All these factors speak for themselves.
Yes, The Mummy Returns was atrocious and Tomb of the Dragon Emperor at best mediocre, but this argument doesn't concern those two.
I could go on, discussing the awesomeness of John Hannah and Oded Fehr, not to mention the fantastic sense of place, Jerry Goldsmith's excellent score and more, but I think I'll rest my case here. I say that for the above reasons and more, The Mummy is the best archaeology-themed adventure movie since Raiders.