The SLS and the STS seem to be the only rockets utilizing SRBs... Why did they choose to go with them over LH/LOX or Kerosene/LOX? Wouldn't it also be easier to upgrade those rockets in the future?
SRBs have a very high thrust to weight ratio, even if they have an only modest ISP. That makes it complementary with LH2/LOX systems that have a relatively low thrust. Early on acceleration is almost as important for over all efficiency as exhaust velocity. For the first few hundred m/s of $\Delta v$, a combined metric of ISP and propellant density, called density impulse, is a good way to rate performance. Considering that, SRBs have an excellent performance.
Another reason to continue with them for the SLS is to use off-the-shelf technology already developed for the space shuttle in order to save money. However, they are going to be upgraded from four to five booster segments for a larger total impulse.
The space shuttle SRBs were the rocket engines with the highest thrust ever made, and that was achieved without particularly cutting-edge technology.
The STS and the SLS are not the only launchers utilizing them, the European Ariane 5 uses solid rocket boosters too. Most ICBMs are also currently based on solid propellants for storage reasons.
Ariane 5 uses similarly large SRBs. Atlas V and Delta 4 have strap on, smaller SRB's to help boost larger payloads than a bare core can provide.
Heck Vega is entirely made out of solids.
The problem is, you need to get off the pad. What do you do, when your initial stack, as needed to hit your payload/orbital targets, is too heavy to get off the ground. You add on a strap on first stage, usually SRB's because they are simple, can be built large to provide copious thrust early on, then get thrown away as they are not very efficient in terms of ISP.
Cost is the primary advantage of SRBs. Mass specific impulse and density specific impulse are largely unimportant to a liftoff stage (and low mass specific impulse actually provides an advantage in acceleration and thus reduced gravity losses on ascent). The "cost specific impulse" of solid rockets is excellent.
The shuttle SRBs produced 11-13MN of thrust for a cost of \$23 million; the hydrogen-fueled SSME (an exceptionally complex and expensive engine, to be sure) cost \$50 million and produced a sixth as much thrust.
The SLS boosters are longer, 5 segments instead of 4, but any recovery-and-reuse features can be omitted, so it should cost less than 125% of the shuttle SRB; I'd guess something like \$28M per shot.
The most feasible replacement for solids for the SLS booster would be the "Pyrios" booster proposed by Dynetics and Rocketdyne; each booster would be a kerosene/LOX tank with a pair of cost-reduced F-1B engines. It's unclear what Pyrios boosters would cost, but it's hard to imagine it would be much less than $20 million per engine, plus the structure.
Because congress wants pork to go to Utah and congress wants to keep engineers who know how to make large solid rocket ICBMs in jobs in case we ever need to build a lot more of them in the future.
Solid rockets are a terrible fit for SLS, not only do they have form for having killed seven astronauts but they are no cheaper than a liquid fueled booster without any hope of having an economically viable way of reusing them (sts booster reuse saved nothing money wise). Block 1b SLS is a heavier rocket with greater thrust than Saturn V yet still manages to deliver less cargo to tli or gto than a 50 year old design.
Solid boosters work great to tailor performance on expendable rockets like atlas and they brilliant for ICBMs. They are pretty naff IMO for high performance heavy lift - they are too dangerous, uncontrollable, expensive, poorly performing ( mainly with regard to ISP).
Not a fan.