What would actually happen to queue times if true solo queue was added
TL;DR Dynamic queue times will definitely be longer, but solo queue times might actually end up being shorter
A lot of people like to say that adding solo queue would increase queue times dramatically. While that's partially true, it's really only the dynamic part it's true for. Adding solo queue would affect the queue times for dynamic and solo queue in completely different fashions. Let me break out the logic.
Dynamic Queue: Naturally, almost all of the solo players currently playing dynamic queue will switch over to solo queue if it's added. The dynamic queue matchmaking system will generally find 2 premades of similar sizes and skill, put them on different teams, and then use solo players to fill the rest of the spots. Without solo players, their fill algorithms will suffer greatly. 4 man premades will especially suffer as solo players are a requirement to get them into matches. With solo players missing, the queue times for 4 man premades will skyrocket to the point where most will probly quit before getting into a match. 2 and 3 man premades will suffer a bit less as they can be combined to form teams of 5 and stuck against each other. But without the solo fill players, their queue times will also increase significantly, but probly not to the unplayable amounts as 4 man premades. 5 man premades probly won't suffer much at all. According to a post a while back by Riot, 5 man premades are only not matched up against another 5 man premade 1.5% or 3% of the time. So their queue times will only increase by that percent.
Solo Queue: There's a few variables that could affect solo queue.
First, let's take a look at the matchmaking algorithms. This is fairly straight forward. You find 2 players for each role with a similar skill level and stick them in a match together. Compared to the algorithm for premades where you have to include the skill gaps from members of premades and try to find similar premades and then match them together with solo players that have the general MMR, but you have to increase the MMR rating of the pre-made since they're working together compared to the solo players, and then have a backup plan in case you can't find the perfect match, but you're not sure if you're back up plan includes a different size premade which would add even extra variables to check for in premade skill gaps or solo players which would be far easier to balance but steal solo players from the pool use to fill other matces; the solo queue algorithm is ridiculously simpler, and as a consequence, will naturally work faster.
Second, there's the issue of support players. This is the most unpredictable variable. Currently, the belief is that premades provide the majority of the support players, which does indeed make sense. If this is all there is to it, then this variable will indeed increase queue times as support players are the least chosen role and their numbers will the thing that most hinders queue times. However, this doesn't take into account the number of people playing in premades that only do so cause dynamic queue forces them to in order to remain relevant. Those that switch over to solo queue could increase the number of supports for player if the original belief of supports being primarily in premades is true. There's also the fact that one of the reasons supports are rare amongst solo players is because solo players don't like playing either of the duo lane positions when there is a high chance of their partner being in a premade that will communicate more with their premade even though communication is the duo lane is far more important. This particular variable could go either way, and it's impossible to predict, but it's the only variable that would actually increase queue times for solo queue.
Finally, as has been made apparent, there is a significant different in queue times for tiers will lower populations. That is because the complexity of the matchmaking system for dynamic queue is only worse when you have less players to work with. Premades at high levels are only compatible with certain other premades and solo players. And then less players there are in those tiers, the more often they won't be able to find matches right away and have to keep repeating the algorithm till matches premades and solos show up. For the higher tiers, the simple matchmaking system of solo queue is almost garunteed to decrease queue times a significant amount.