It is an interesting proposition.
But "work" can mean two different things here.
The first issue is is can a low income railcard work to achieve an objective? And is a low income railcard the most effective way of achieving the objective? There might be better ways of achieving the same objective, it is the end that's important not the means.
Of your two different objectives, a low income railcard will probably do more to assist groups of people who face barriers to rail travel than it will to generate business, because by definition low income people don't have much money to spend. There are probably other better ways of generating more business.
The other issue is can a low income railcard work administratively? How is eligibility decided? And how is the railcard withdrawn from people whose financial circumstances improve, so that they no longer qualify?
Where the line should be drawn is the question. Personally I'd like it to be targeted at Theresa May's "Just About Managing's", rather than reserved just for those in abject poverty.
In terms of proving eligibility, I propose that people would present a benefit or tax document from the previous year every time they renew.
I contend that all railcards generate business from people travelling when they otherwise wouldn't do, whether that's their core function or just a by-product.
How about a "rich *******" railcard where you have to pay double (a bit like first class on Southern)? Could be a status symbol amongst the arriviste.
More seriously there's a problem here. If we're going to use the railways for social engineering then the *actual* marginal tax rates in this country are like a bloody yo yo. The ones that get most attention are the 100k withdrawal of personal allowance / childcare cliff edge and the 50/60k child benefit withdrawal but there are pernicious ones at low income too - a cliff edge for carers where £1 a week can cost tens of thousands but also the universal benefit taper can essentially mean a marginal tax rate of 70+%. If you introduce this then (depending on what you are calling low income) for those that use it a lot you will be making this much worse, making that rate maybe up to more than 100% in some cases if they have a significant commute. In which case what incentive do they have to better their circumstances? You have created a poverty trap.
So it's a no from me.
The obvious way to avoid that little conundrum would be to introduce a national railcard available to everyone, however the powers that be seem determined not to do that !
On the broader point, given all the other cliff-edges you've mentioned, I very much doubt that this railcard would lead to someone rationally choosing not to better themselves.
The 100k withdrawal of personal allowance is far above the income level I would target the railcard at.
From a social engineering point of view, this would not only help people who are being burdened with inflation, it might actually facilitate self betterment if it enables people to seek job/educational opportunities elsewhere.