LWM, I'm going to give a slightly different opinion, because I feel like you and Lert got too burned by the US cruiser line and have sorta...developed a great distaste for any of them save the Des Moines or Cleveland, and even then. Them and the St. Louis.
From what I've seen of iChase and other youtubers, the Indianapolis is a very sneaky cruiser, a slimmer Pensacola with one less turret but only one less gun, and a massive AP punch which punishes anyone who dares to ignore even the basics of maneuvering. Yes, there are plenty of spots where you can simply shoot into the superstructure and people moan and complain about how the cruisers don't have any armor, but really, against BB guns, they don't, and for most cruisers mobility is as vital to life as it is to destroyers.
Pensacola is hampered by several things: totally glass hull, giant middle finger for concealment, and the fact that for guns, it doesn't have that quick of a reload to compensate for the fact that it doesn't have torpedoes. It has pretty good HP, the guns hit hard, and overall, she's very comfy if you can deal with her flaws.
The Indianapolis, on the other hand, trades some comfort for a massive boost in range, concealment rating, gun comfort, and some actually rather serious hull armor if you're going bow-on(which you cannot do in the Pensacola.) I have fought gun to gun with an Indianapolis in my Atlanta, and it is pretty harrowing to say the least, with the AP punch providing some scary moments where I thought the citadels would completely obliterate my hull even bow on. AP shots from cruisers with 152mms and even 203s will find Indianapolis' front hull nearly impenetrable, where as good wiggling from the pilot of the Indy will provide a tricky target either advancing or reversing with the forward set of guns going off. However, if you're that close where bow-on is your thing, that's a big problem because it means you might be giving delicate sides to most things which can end you.
Edit: removed this section because it's irrelevant and MrDeaf has kindly provided counterexamples to the claim that was here. Refer to my reply and you'll probably understand what this erroneous claim was.
The benefit of Indianapolis' godly awesome AP rounds? Just watch as most cruisers facemelt underneath the barrage of 4600 damage AP, and battleships flinch as you fire through the poor armor near the bow and stern to rip into the ship. I did this with a Pensacola because the NoCo ignored me, but knowing that's what the Pensacola can do, I'm sure the Indianapolis can do better.
It's still glass, it's still an American cruiser, it has relatively poor secondaries, terrible armor overall, and it has a poor reload for what it should have, but to be honest it's a lot better than the Atlanta though the Atlanta is fun. Unlike the Atlanta, it is cruiser play at the level, not oversized destroyer such as the Yuubari.
Maybe the tone here is a bit too harsh, but the Indianopolis, imo from watching players use it and fighting against it, is a better Pensacola which makes good credits and prepares you for the rest of the line.
Wargaming had their chance to rectify this and put the cruiser Wichita in as a premium, but apparently the single cruiser of her class and the predecessor of the successful Baltimore and Des Moines cruisers is not good enough a reputation.