I think the distinction between utility mages and other types is that utility mages already offer something that is totally unique and that mobile mages don't have really good access to (e.g. no mobile mage could have Anivia's area denial, Orianna's ally wombo combo potential, or Morgana's massive CC and utility), whereas most immobile mages tend to suffer mainly because, due to both mobile and immobile mages primarily supplementing damage, there's less of a distinction between the latter two's contributions, which makes immobile mages feel bad when mobile mages can do more or less what they're meant to shine at, on top of having more maneuverability. For that reason, I also think Xerath and Lux are unlikely to receive too many changes, if any at all, because their unparalleled range is also a clear factor that sets them apart from mobile mages. On the other hand, Swain and Vlad are likely to receive changes eventually, despite having power mobile mages don't (i.e. sustain), mainly because their self-healing is really poorly gated and not as cool as it could be.
A lot of what you posted looks fairly spot-on, though, and on top of that I think/hope the immobile mage pass might put an emphasis on their AoE and/or combo capabilities, something you brought up especially on Brand: a common feature of all mobile mages (e.g. Ahri, Azir, Leblanc, who probably counts more as an assassin overall, Lissandra and Ziggs) is that their damage tends to be mostly focused on a single enemy. Mages like Brand, Heimerdinger and Karthus all have tremendous AoE potential, but so far have also remained mostly focused on killing enemies one at a time, which not only limits diversity of gameplay, imo (if there's one class out there who should encourage catching multiple enemies at a time or nuking different opponents over the course of a fight, it should be mages), but also forces those immobile champions to set themselves the same goals as mobile mages (i.e. "kill this one target"), but with fewer tools and power that doesn't directly help when achieving said goals (often, killing multiple targets at once feels more incidental to focusing a specific enemy, when it should likely be the main goal of those champions). Enabling greater AoE potential on these champions, at the cost of other factors (e.g. less single-target burst, combo gates on their AoE potential, etc.) could help them distinguish themselves as great anti-crowd damage dealers.
On the opposite end, champions like Syndra, Viktor and Veigar are capable of popping certain champions in a single ability rotation without needing to be too far ahead (Brand too, though to a lesser extent, so he might need to lose some burst in order to have more AoE, or vice versa, in order to differentiate himself more), which is already something mobile champions are less likely to do without a large gold and level lead, but that ultimately means a mobile mage can do everything an immobile combo mage can do if they snowball hard enough, except with supplemental mobility to make their own comboes easier to set up. I'm less sure of what could be done for them, but I think the main lever to pull should be their ability to punish people for falling into their combo trap: immobile mages have no tools to set up their comboes other than their range, unlike mobile mages who can get themselves at just the right spot, so if they do manage to pull off their comboes, especially against a roster of champions who's become increasingly mobile, and therefore better able to evade their abilities, they should be able to dish out some of the best, if not the best burst in the game, perhaps to a level that could nuke even tanks. They should likely be less effective if their comboes get dodged, e.g. via longer cooldowns, slower nukes, weaker AoE and the like, as a result, but with a heavy focus on punishing comboes they should be able to provide power mobile champions couldn't touch (area denial, at the very least).
As for sustain mages (Fiddlesticks, Ryze, Swain, Vladimir, perhaps Cassiopeia and Morgana, though they rely a lot less on their self-healing), they already have pretty visible and unique strengths (self-healing, great DPS, superior resilience for a mage) and weaknesses (sub-par range and burst for a mage, low mobility for any champion), but the main issue with most of them is their gameplay: the Cass and Ryze reworks didn't quite hit the mark, Fiddle's been abandoned by recent jungle itemization and has a ton of anti-synergies holding him back (e.g. his Q making enemies run away from his W, once fear was made non-random), and both Swain and Vlad have such poorly controlled self-healing that they'd be absolutely horrible to deal with if they received proper buffs. A big part of the issue here likely comes down to the problem of drain tanking (how do you balance a champion whose durability is based on healing over time?), and if Riot manages to find a way to give these champions proper sustain and DPS, with both sufficient power and counterplay, they could potentially also solve the issue of other sustain champions, like Warwick and Dr. Mundo, without having to resort to Grievous Wounds, which isn't a good mechanic and hasn't proven to be very intuitive since its recent reintroduction to marksman itemization.
will see the most significant changes,
and 
becoming a notably modernized.
Minor. Tweaks, possibly on W.
Minor. Tweaks, possibly reworked Passive.
Minor. May see some tweaks.
Minor. Retuned power-curve and improved Passive.
Minor. Tweaks to Passive.
Minor. Tweaks to R, maybe little more than aesthetic ones.
.
.
.
Extra: Some mages that likely won't be included, but could use some love
A really weird character overall, really needs significant kit improvements and better distributed power budget.
A unique character, but desperately needs an entirely new Passive and E. His Q might be better off reworked a bit too.
Skill floor is really a bit too high. 
Could possibly see them do tweaks to Heat mechanic.
Could use a Passive that's more interesting, but not much else. 
Mechanics could do being condensed a little bit.
.
.
Edit: Some commenters suggested "utility mages" may not be included in the rework batch, which makes me less sure of what will be included. The line between mage and utility-mage is blurred at best. However, this could suggest that
etc level changes are perfectly fine. Especially in terms of voidlings, as AD Malzahar is getting pushed out with all the attack speed and crit chance being dumped onto most AD items.
, and 
?
is perfect <3
