Problems and Solutions
This game is riddled with issues right now. I get that we're in preseason and it's a testing ground for all the crazy stuff, but we've all become aware of the issues in the game right now. Let's have a look at some general issues and how we can resolve them. Several of these issues are linked, and most would have a minor effect of slowing the game down, which would contribute to a noticeable amount of several of these changes were implemented. Feel free to shit all over my suggestions, and feel free to add your own in the comments.
Problem: Arcane Comet deals too much damage (Aery less so since the nerf).
Solution: Increase MR for everyone so they're inline with the old scaling MR runes. Perhaps mimic this with a small amount of MR/level as well. The damage on these runes aren't too high, but rather we're taking more magic damage than before, meaning these give a lot of poke early even to non-AP champs like 
.
Problem: Towers die too quickly.
Solution: Buff tower armour. Simple really. First tower gold is a great incentive to push early but it should take more to achieve the sizeable gold bonus.
Problem: Early tower dives are too easy to perform early, and this translates into a first tower gold lead snowball.
Solution: DON'T increase tower damage - they deal plenty early on. Instead, towers should grant some sort of small AOE bonus around them, perhaps a small armour + MR bonus. This will make it harder to dive and delete squishy champions (bot laners being the usual target), as it'll take more of a time commitment, meaning you take more tower hits. It'll also make sieges a bit more challenging overall, slowing the game pace slightly.
Problem: ADCs pop off too early.
Solution: Increase cost of several ADC items to delay their power spikes. Statikk Shiv could safely cost 2900 or even 3000 gold and be worthwhile. Increase IE cost by 100g to 200g. ADCs SHOULD be the strongest class late game, but their true power should come at around 25-30 minutes into the game. This will also have the added bonus of slowing the game down a bit, and making lane-focused ADCs like Caitlyn more viable again (as much as I hate to lane vs her when she's strong).
Problem: Press the Attack is too strong, and overshadows lethal tempo
Solution: Make the 12% bonus damage effect of press the attack only apply to your allies. It already does decent adaptive damage, and it would be good to differentiate it more from lethal tempo (the latter is solo-focused damage, the former becomes teamfight-oriented).
Problem: Minion dematerializer is weak and unsatisfying.
Solution: Buff its values, and/or make it work on small jungle monsters. Doing something like dematerializing a small wolf would make you deal more damage to all wolves in the course of the game. Give junglers more incentive to go into inspiration, maybe if they've got bad early clears or are farm-oriented. Or just replace the rune entirely with some other push-oriented rune, which might be a better option.
Problem: Kleptomancy Ezreal
Solution: Change Ezreal's Q to only work with lifesteal and spellblade effects instead of all on-hit effects. This will keep all his core items for various builds intact while removing abusive edge cases, which we've seen several of in the past. Note that Muramana will still work as this triggers on single-target spells OR autos.
Problem: Tanks are overshadowing other toplane options.
Solution: Tanks are supposed to be the kings of team fights. To trade off against this, they need a weak lane phase. Champions like 
and 
are bypassing this weakness entirely thanks to having very high sustain and/or damage. We need them to be more like Nautilus, who offers great CC and tankiness but is lacking in damage and lane presence. Reducing base values but increasing scaling will work wonders for emphasising their early weaknesses while keeping them about as effective as they are currently.
Problem: Fighters in particular struggle top lane
Solution: Nerfing tanks is part of the solution, but also we can nerf 
. This item is too cost-effective, and 
is too cost-ineffective. Remove the grievous wounds effect from Bramblevest, and just keep it as part of Thornmail. This will mean that a single cheap item won't shut down lifesteal duellists like 
immediately after first back. Hard counter items are important, but if mid laners have to shell out an arm and a leg to get 
to win a hard matchup, so too should top laners. Fighters being more viable will also mean that ADCs be more at risk until their tanks also hit their stride.
Problem: Fighters and bruisers lack meaningful rune options, and feel like they just use other classes' hand-me-downs.
Solution: By now Riot will have tons of data on which runes are unpopular and under-performing (see Minion Dematerializer), or have high functional overlap (Press the Attack and Lethal Tempo, Zombie Ward and Ghost Poro). This opens up opportunities to revamp these options and make them into something that can benefit classes that are struggling. I'm sure there's at least one rune in each tree that nobody would miss, which could be changed to make fighters and bruisers feel more included in the new system.
Now I'm sure if some of these issues were address there would be other issues (assassins would run rampant if tanks became less prevalent and powerful for example), but I think any suggestions are good. Let me know what you think.