First of all, I'm about to piss all over your idea -so, sorry for that. I think it's great that you're thinking about stuff like this though. I'm all about moving forward and improving. Unfortunately, I think this idea requires too many compromises, doesn't provide enough benefit, and either raises the barrier of entry to flying basilisk or requires that a cap chain still be maintained.
First, let's talk barrier to entry. The fit requires Logistics Cruisers V just to get started, which will limit the pool of available logi. Of course, most pilots do quickly train logi V, but this will slightly increase the chances of running low on logi.
Second, the fit makes several compromises
7% less repping power
32% more expensive than the opti Basi, and 274% more expensive than the minimum fit
Buffer EHP is lower than the opti and minimum fits by 7.5% and 29.4% respectively. This is combined with diminished repping power for the fleet -which is not inconsequential considering logistics cruisers are already the most frequently lost ships.
No room for a sig amp (which reducses lock times, significantly decreases the chances of being jammed by Niarja [still quite likely to be jammed by the 3x arnon though], and grants up to 2 extra locks for pre-locking agro magnets and dealing with split agro).
No room for a ReSeBo, which greatly helps the DDD to kill Niarjas -which, in turn, improves fleet safety. FC's often fit ReSeBo's, but up to three scripted, faction ReSeBo's will have an effect on lock times.
Finally, it just doesn't give enough benefit. New logi often fumble with the cap chain, and older logi sometimes make mistakes, but it eventually becomes as easy as locking and shooting targets, and issues are (usually) rapidly addressed. Moreover, if 1 unstable basi joins, then a stable basi still has to give them cap. And if more unstable basi's join, you haven't actually eliminated the cap chain, you've just exempted yourself from it through significant compromise. Besides, the biggest PITA of flying a basi isn't the chain, it's slinging cap to all those thirsty vindis and T1 blaster boats. To me, managing the cap chain is just one those skills you have to learn, sooner or later, as a logi pilot.
Oh, and I haven't done the math, but the neut resistance from the cap battery might make a significant difference when it comes to the niarja's and deltoles, but probably not the outini's. So, this might be a plus, but it still isn't going to be enough to offset the disadvantages.
TLDR: You're not alone in liking the cap stable basi, but I can't endorse it... for now.
At Evesterdam, CCP said that they would be introducing Saviors (implants that reduce logi rep cycles), and rebalancing cap mods so that they have bigger effect sizes, but are subject to stacking penalties. This means that it may be possible to get basi's cap stable with fewer cap mods in the future. This, in turn, could free up slots for ReSeBo's and Sig Amps. Of course, all that being said, I think the fleet would probably get more benefit from logi with Savior Implants, than the elimination of the cap chain.