After reading through the many interesting and useful insights on this thread, I thought it perhaps worthwhile stepping back a bit to consider the matter from the perspective of general principles, for example:
(1) The current episode with Adobe is a telling illustration of why competition in markets is important. A great deal of abuse can be leveraged on the strength of incumbency without actually breaking laws, and competition is really the only effective tool we have to constrain it. So if a group of highly intelligent and well-healed people are conjuring-up the idea of expanding choice in the market place, I think this is long overdue and deserves wholehearted support from all members of the imaging community who care about such matters.
(2) We have been educated - in good part by folks such as the late Bruce Fraser, yourself, others, of the major advantages of parametric editing. Ever since the introduction of LR1, the progress of LR has been to push the "boundaries of the possible" in respect of the things one can do with images parametrically. We know this is an evolutionary process that has occupied the talents of the best mathematical, programming and design minds in the imaging business, and I for one have no knowledge or reason to believe that humankind has necessarily reached the wall in respect of this evolution.
(3) So in light of (2) above, as general guidance on the overall technological thrust of a new initiative, I would like to see it focus primarily on parametric functionality, combined with modules that can convert the image to pixels and perform pixel-based editing for those things that people consider essential and cannot be done (yet) in a parametric manner. Then, as the new application progresses, part of its "design motivation" would be to gradually eat-through those pixel-editing requirements by incrementally doing more and more parametrically.
(4) You will doubtless recall that the genesis of LR was to create an application for photographers that would shed the PS baggage photographers don't really need, and be a "simple" bare-bones photo editing application. Well, Mark Hamburg said he may have failed when he was called upon to commend us to Martin's excellent 600 page manual on the basic and creative use of LR! But of course he didn't fail. It was brilliant and still is. There is actually nothing in LR that I don't use, and by now my trips to Photoshop are truly very limited. The incentive for me to upgrade Photoshop whether on subscription or not is close to zilch. So the bar that needs to be exceeded by those creating a new application is "LR 5 and some added stuff that rounds it out". Many good ideas have been posted above on what some of those things should be.
(5) On the functional/commercial aspect of it, I think some general principles of the commercial and technical arrangements would need to be established up-front, well communicated to the potential client base, and then respected in the implementation as rigorously and for as long as circumstances permit, because TRUST is going to be a very essential core value in the success of a fledgling enterprise. I frankly don't have any druthers about whether the marketing basis would be by subscription or perpetual license, but the one fundamental aspect of it that must be respected is that if it goes the subscription route, at the end of a contracted subscription period the subscriber will have the right, even if for an added fee, to obtain a permanent license key to the last version he/she used at the end of their subscription, in order to preserve all the access and editing capability they had up to that point, so that all the work they did on those images would not be at the mercy of a process and future cost path beyond their control. This is the core sticking point with the current Adobe scheme, hence a new company marketing a new application just needs to be smart about this.
(6) Sorry - one more point - learn from the more egregious aspects of Adobe's license agreement for CC, how NOT to deal with people.