Controversial perhaps but you do need to ask these questions occasionally to gather some understanding of impact.
As this is a value judgement as to whether to do this or not, then surely you will have a guidance document of some kind that states what the aims of the product currently are (high level design objectives), against which you and any other decision makers can evaluate the idea, both before and with any feedback you get. If not, it might be helpful to create one at some point. It's a good reference point for why you have made previous decisions.
From a user's perspective the value they receive through being able to install, update, manage and administer through a web interface with nice easy guided layout is all about giving them fantastic product utility and as others have said that's what brought me to your product a while ago, despite the early feature set in terms of overall function. Increase complexity and you will reduce usage by small outfits with lower skill levels.
You don't actually say what this is required for, other than to simplify development effort so it may be that you are seeing additional support requirements with lower skilled admins out there, you may be seeing hoops to jump through as developers that you could really do without based on previous technical decisions or many other reasons. These have multiple potential solutions and I would urge you to consider alternative solutions because people really do value what you have given so far and if you can crack this you will be able to deliver what they already have and love and continue to improve it going forward.
As an example of how this can work, I run Joomla sites and there is a fantastic piece of software called Akeeba Backup. which is pretty much the go to solution for backing up, transferring, restoring sites, databases etc. It's had to work round many issues with hosting companies setups and at the front there is the easy web way (which actually gets better over time) behind the scenes there are multiple string and glue methods to cater for the less well known approaches. Nik I know gets very frustrated with many of the same issues that I guess you have to deal with but rises to the challenge each time and as he finds a solution the product becomes more indispensable to a larger user base. I don't know but having seen a number of incarnations to the product I suspect he's had a couple of ground up re-writes of parts of the solution. I contribute through my support subscription, which I need less and less but it keeps him going and the value the product gives me easily justifies the low cost.
To answer the direct question:
Specifically for me, it will kill it as a product on three websites (personal and charity) with two hosting companies. Not because I don't have shell access ( I don't) but because I try to leave sites that someone else can administer as a simple user should I not be around.
That of course will give me a reasonable degree of pain in researching alternatives and then installing and transferring content etc.
So... my vote is No..