As Reaper Soraka stated, coming up with a way to prevent them is the major issue since it's a Free-to-Play game. TL;DR at the bottom, just realized how long my post was sorry!
If the game becomes subscription based, a large portion of the community becomes isolated and unable to play. One of the large reasons people tend to create a smurf is to deal with the anxiety of losing LP/Rank/MMR/etc. on their main. Say someone has 500 games played in Platinum 5 and is at 0 LP at risk of demoting. While it's not exactly productive for them to play against Bronze 5 players and stomp their way through the ladder, the MMR system is usually pretty good at matching players of a similar skill-set pretty quickly. For that Platinum 5 player, playing on an account that is at Silver 2 and quickly grinding the ladder to reach Gold or higher is rewarding to them and helps foster a place in their mind where they feel more apt to play and continue grinding. Most games try to do this as well, as it's a healthy way for the player to re-learn the ropes and try out different situations without being at risk of losing the amount of time they spent to achieve their goals on another character.
On the flip-side, it's difficult for those that they're playing with to have a fun time if they're consistently matched with "smurfs." For example, when Arenas first launched in WoW, every team would start at 1500 rating and there was no personal MMR saved. You would get "Arena Points" every week based on the rating of the team. So high-ranking players (Gladiators) would often sell their teams as a modest rating to lower rating individuals as a way to circumvent the system and allow them to get their gear faster. This system USUALLY worked fairly well, as you would quickly be able to "outplay" your opponents at the lower ratings (or simply out-gear them to the extreme) for the higher rating individuals that have already accomplished their goals. However you'd often end up with Gladiators at 1500 rating facing one another to attempt to grind these teams out, and anyone who actually was at 1500 rating or below would basically be fodder for them. This wasn't healthy for either set of players, as it made the higher rating individuals have a rough time getting a team to where they wanted it and the newer lower-rating players would have a miserable time climbing an uphill battle and forcing them to queue-dodge if they knew someone of much higher rating was "boosting" a team up around their MMR. This led to personal MMR being in place rather quickly and Gladiators would only face similar MMR players, making it very difficult to climb a new team and reinforcing the whole "don't stomp new players please."
For League, the way they prevent this is by requiring a leveling system to play ranked. While level 30 isn't incredibly difficult to achieve, it does require a rather significant amount of time invested (unless they bought the account, in which case it can be banned for obvious reasons). Usually by this time, the players end up having a somewhat balanced MMR for Normals and why the dreaded "smurf-queue" exists - where players under level 30 feel entitled to boast their "main's rank" while trying to make their way into ranked. Stepping into Ranked is where the main problem with their MMR begins, as it will bounce around at a VERY volatile rate. Someone of a Gold 5 rating is likely to get placed into high Bronze or low Silver depending on how their placements go as there isn't a lot of MMR difference between their main's rank and smurf's rank. This is where a lot of problems begin, as although the MMR difference is only a few hundred points away, the skill difference is VERY drastic. These players will be gaining ~20-30 LP for a win and falling ~10-15 LP for a loss until they balance out, and will often sit in a lower MMR than their main for a decent portion of time. This leads to them being matched up with similar lower ranked players for a decent portion of time and being able to "stomp" their way in nearly every lane; provided they aren't matched with someone of an equal or higher skill level that is doing the same thing they are.
There's also the occasional individual that only wants to boost their own ego and play for KDA to look fancy on paper, while caring little to none about the team's well-being or destroying the enemy Nexus. It's easy to go 10/0 on Fizz (or someone similar) against a lower-ranked player, it's much harder to transition that lead throughout the map and capitalize on your advantage. These are the individuals that generally tend to create the most problems and raging in Ranked, as it's very demoralizing to play against them. Usually they will kill you, go back to base and get stronger while you're dead, come back and kill you again, rinse and repeat. It makes it difficult to have an impact for you later in the game, but at the same time frees your team up to do other things and capitalize on their greed. I can recall a specific game a long time ago where I was Rek'Sai jungle against an enemy Shyvana who ran Ignite/Exhaust without smite and had 0 goals other than to pad their KDA and flame their team (or so it seemed) while boasting about how much higher rank their main is than everyone else in the game. They ended up something like 14/2/0 losing the game in the process as I was able to have a drastic effect on our lanes (and subsequently killing their Towers/Inhibitors/Nexus) while the Shyvana was busy power-farming and only running into fights where she should easily pick up a kill and leave - never backing up her laners or attempting to help them when we inevitably dove them. Those type of players are easily punished and tend to get stuck in a lower MMR than they belong, as they refuse to accept the "team" aspect of the game and are able to continually make leads for themselves while throwing it all away in the end. It's nice to be up 7k gold on your enemy laner, it sucks when you die at 60 minutes and have to wait 79 seconds to respawn while the enemy team crushes your entire base being unable to use your gold lead - effectively putting the enemy team at a MASSIVE gold advantage since you're the one carrying it all.
TL;DR: It's a team game at the end of the day. It's very difficult to limit smurfing being free-to-play as well without compromising the current MMR system of every game mode having its own MMR. Someone that kills it in Normals up to 30 might be placed into Diamond and be crushed for 100 games straight until they fall. A lot of people create smurfs to deal with Ranked Anxiety on their main. Those who are significantly higher rank and play a team game tend to climb faster and get out of lower ELO quickly (skipping divisions often). Those who are looking to pad their stats tend to get stuck in lower ranking divisions and sit there causing more trouble for the system.
