Yeah, I get that it's nice to just play alone once in a while when you're not feeling in the people kind of mood. We all have those moments and there is nothing wrong with that or just wanting to be "the best" by your self. Though In my opinion, it doesn't really have much of a place in this game thematically or mechanically.
For one, none of the Legends abilities are designed to work for solo play. Some like BH, LL, Caustic, and Mirage would work without any real downsides but no one could make a case for using the Ult of any other legends on a regular basis. "What about the movement abilities like jump pad, portal, and zip line" I hear you say? While yes, they are all useful in squads, they also have their downsides. Downsides that are no longer offset by the advantages they granted your now non-existent squad. The fact they are all VERY loud to set up and use, which in squads is offset by the fact that you may still catch one or two players of an enemy squad off guard where you'll be descending on them with fully prepared killers, means in singles you're now announcing to a much more aware player "hey, I'm here and am either coming to kill you or am very hurt and am running away!" on top of that there is the already existing downside that anyone and everyone can follow you. Bang and Gibby Ults would be used even more sparingly than they already are, being saved only for panicked escapes and the extremely rare occurrence of more than three enemies being in one place.
Second, if your issue is with the quality of your teammates, then your prayers are already being answered. We are being given ranked in season two and with it, comes the promise of playing with people at your level. Sure you'll potentially still run into people who when and got themselves boosted once in a while, and yeah it'll be just as annoying but, won't happen as often as matching with bad players outside of ranked. Beyond boosters though, I know there will still be people who complain about the "quality" of who they get matched with in ranked. For them, I have no real answer besides "deal with it" or "queue with a premade squad" because, in the end, they would boil down to two kinds of players. The ones complaining about being matched with someone who has a clashing playstyle (ie. hyper-aggressive rushers and ultra passive campers matchmaking into a squad), which is fair and frustrating, and the ones who just can't accept they're actually bad or refuse to accept any amount of blame for things going wrong.
Finally, let's be real for a sec. Apex is a game, a great game by a great developer. One which managed to capture the interest of a nearly incomprehensible number of people. It's amazing, and though we have all become enthralled and grown so invested in it, ultimately we were captured by a vision. The vision of fellow gamers turned developers and employed by Respawn entertainment. It is thanks to them that we get to have all this fun in this awesome game and they deserve that credit. Their vision, as far as we've been told, was and is to make a great first-person shooter battle royale, which doesn't focus solely on shooting but, also tells a deep interconnected story that shares a universe with another of their much-loved games. We have the right to let them know how we'd like to play their game but remember the choice is their own and according to them, singles makes no sense in that world right now.
I short, the reasons singles cannot and should not be added are: While playing it nearly an entire dimension to the gameplay would be lost in the form of most ults being rendered useless, the complaint that your squadmates aren't up to snuff will be essentially null and void, and it just makes no sense at all for singles to be a thing lore wise at this point. It would just be a much less dynamic experience and at that point may as well not even be Apex. If you want a singles BR mode, it may be better to ask them to add it to their next Titan Fall title.
Since there are some ways they could potentially work it into the lore of that. Like maybe operatives from various factions or from the same faction got lured into a trap without knowing the others would be there. While something like a bombardment or toxic gas encroaches on the only viable extraction point. The ensuing panic leading to all involved assuming the hostility of the others and fighting to secure their own way out.