Can't really think of any frontloaded bar that's as reliable/consistent for the AI to use.
Invoke seems the closest atm, but having Zhed run it before my char got to unlocking Norgu, I found I've had to babysit its invoke&attunement quite often. AI also feels way too clumsy with RoJ usage/placement without relatively excessive micro or specifically building my own bar for my liking (though ironically, still smarter than 9/10 of pug randoms); this is for my mesmer char, so SoH doesn't matter. I tried looking at necros, but the options are pretty crap for non-physicals. Never realised the AI options for caster players were so mediocre without mercs, since necro is my only pve caster char & ap/mop + spears/paras was an absolute no-brainer for that.
I can run whatever myself - keystone/surge/ap/EC/PI/etc. will spec for the zone or whatever mood I'm in, so just looking for a low maintainence pewpew hero bar to fill in #7 slot. The other AI bars are basically the main 5 from here or mm -> ST, but defensively tweaked like mop/splinter/PoD -> wow+rejuv/wowx2/IV (prefer drain/shatter to PoD generally tbh) & a burst monk. FB! can always be put on the SoS instead of #7 if necessary.
I'd also rather not change my Raz to me/ because I like the option of switching in the ST on demand.
Non-mes alternative to esurge bot
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Plutoman
Invoke is pretty good - use attunement and aura of resto, and he'll generally have an enchant up. Energy's fine. It also is good with Fall Back.
FoxBat
A single physical for your splinters to get off quickly/efficiently can be worth it (yes you'd have to re-add it to your bar...). Minions have slow move and attack speed and aren't necessarily on the clump of targets you're on, and the AI does not prioritize your vanguard sins over minions, but they will prioritize your martial-wielding party members. The page already listed a mostly support-ish paragon that can do this, you can give him volley/barrage in packed areas to build adren faster and ensure splinter is used ASAP, you could run it as ranger instead for more damage/less command.
Cantos
You could try FoC like in this build.
Jeydra
Invoke Eles are as good as and arguably better than stacked ESurge Mesmers, I suggest you use them. They don't spam Invoke on cooldown (sadly), but they generally don't get exhausted either (unless getting targetted by enchantment removal - sad thing about playing Ele).