The Electoral Collage is called out in the Constitution, so eliminating it would take an amendment and all of the ratification that goes with it. There are some work-arounds, however.
The Electoral College was established to provide a fair mechanism to enable states of varying size to be represented when voting for the president. It's been since mutated from district-based to state-based drives. In 48 states, it's a winner-take-all system, where the popular vote in the state decides where that state's electoral votes go. In Maine and Nebraska, they divide their votes between districts. Additionally, in 1929, Congress set the size of the House of Representatives, which drives the size of the Electoral College, to 435 members, instead of the previous representation by population size.
This has fixed (as in solidified, not "rigged") the electorate, turning the lean heavily toward smaller states.
The following demonstrates how this skew provides some imbalance. The graphic below is the county results for the 2016 presidential election. It isn't exactly following the Electoral College divide, but helps clearly show that when you shift from "how each county voted" to "how the population in each county voted," the swag given to the smaller populations grows quickly.
This could be improved a little by turning the bubbles into the proportions for each county, which would likely still show an even closer blend than happens.
So how to solve this? I don't have an answer, but I've seen some suggestions that make sense.
On the forefront, rectify the size of congress. Change the representation to actually be representative of the population. Maybe this means allowing a larger or scaled proportion of each area. This has an upside where representation can again be, well, representative. As cities have grown, some of the constituencies have also grown, equal to the populations of states, in some cases. This would surely give a few more for the spread-out states like Montana and Wyoming, and a lot more for the dense states on the coasts.
Related, fix gerrymandering. Eliminate it and try to actually or arbitrarily represent people. Sometimes, geographic divides make sense, and will happen at state or county or other borders. But the block-by-block and even house-by-house divisions that happen now are ridiculous, and exist to serve the elected, not the represented. This doesn't directly go to the Electoral College, but if you're going to fix the one, fix the other.
Really, if that's too hard, or turns out to make things worse, shift to a popular vote. Make every vote equal, whether from a city or farm, coast or middle, . Since the Electoral College is outlined and mandated in the Constitution, changing it is very difficult. It does leave the mechanism for choosing electors to the states, however. The National Popular Vote movement seeks to rectify this by having states wait to declare where their Electoral College votes go until the nationwide popular vote winner is declared, after counting all (or enough) of the votes. Colorado joined in this last election, making 16 states for 196 Electoral College votes follow the national popular vote. According to the NPV website, this will take effect only when 270 Electoral College votes are in the pact.
Still, until enough states (and DC) join the movement, it'll be the case that there will be battleground and swing states. And even if enough states join to meet the 270 Electoral College votes necessary to make the battleground states less powerful, there would still be battlegrounds, as the high-density populations would become the new battlegrounds. Maybe that's better, since those discussions still propagate to other areas with the readily available media we have now.
Maybe it's time for something radical. Introduce something a little different, like ranked voting. This would not have been feasible before computers, but it's easy to make happen now. This offers real opportunity to break from the two-party system we have now, which was also a dream of the founding fathers. Some rhetoric incorrectly identifies a two-party system as part of the Constitution, when in fact it is neither declared or denied. Allowing a ranked voting system not only allows for more parties, but also more candidates in a party. Instead of the paring-down we have now with the election year primaries and reductions of tickets, most or all of the candidates could remain on the ballot until the end. Voters could rank the candidates they'd like, and clear algorithms could choose and adjust the rankings as additional votes come in.
Something's got to change. The system we have now may have worked when it was last "fixed" about a hundred years ago. It's been breaking and getting worse since.