What if you love your field but can't take the heat of academia? Imagine "a person" who may or may not be brilliant in her field, but certainly has new things to contribute, some of them (in her opinion) fascinating.

Imagine she adores her field, relates to it spiritually, and has been convinced for years that her life purpose is to do this research. She cannot imagine spending her time on this planet in any other way. 

Of course, she has poured hours into it already, devoting her undergraduate career and much of her personal time to her area of interest. But she knows that it takes years of full-time commitment, study, and mentorship to become an expert in a field and to become qualified to break ground in a specific area.

But suppose it is not in her nature, nor particularly within her abilities, to meet the demands of today's academic culture. She is absent-minded and spacey; she is idealistic; she is in certain ways immature. She crumbles easily under stress and is psychologically vulnerable. She has difficulty making time for everything even without the demands of a graduate or postgraduate workload. She hates filling out forms and (especially) soliciting recommendations, even though her kind and charitable professors are always eager to write for her. 

Please answer one or both of these questions:

A.

Should the person in my example "go into academe"--that is, should she go to graduate school for an academic PhD? If not, what should she do?

B.

Does the "absent-minded professor" exist anymore, and if so, how do/did they get through the hurdles?
I think the heart of this question comes to what this hypothetical person actually wants when it comes to "doing research."  This could mean a lot of different things, but when I hear people speak vaguely in this manner, the notions often roughly categorize into three clusters:


Exploring ideas relating to a field of knowledge: To explore ideas and communicate about them a person can readily participate as an amateur, working at whatever level of intensity and engagement makes most sense.  There's nothing wrong with engaging on this level, and it can actually be quite important, especially when it comes to communication of scientific ideas (e.g., many science journalists can be considered to engage with research in this way).
Doing work that supports the advancement of knowledge: One can do work that supports research without actually signing up for the full primary investigator load.  Lab technicians, amateur astronomers, and industrial researchers are all people who "get things done" that directly contribute to research and the advancement of knowledge, yet rarely or never need face the challenges associated with publication and funding.  The bigger the research project, the more space there is for people of this sort: most of the people working on the Large Hadron Collider, for example, probably fall into this category.  Depending on the particulars, contributions might require no formal education at all anywhere up to a doctorate and postdoc specialization.
Organizing and leading investigations that advance knowledge: Leading research as a primary investigator is where the serious "heat" comes in, and where a doctorate is definitely required. Here one needs to have not only the technical training but also to be able to deal with strong criticism of one's ideas and to be well organized and capable of communicating scientifically.  Note, however, that "dealing with criticism" should not mean putting up with verbal abuse and ad hominem attacks.


Now, relating this to your hypothetical person.  The two key warning flags that I see in your statement are "crumbles easily under stress and is psychologically vulnerable" and "difficulty making time for everything." 


If "difficulty making time" means the person cannot really commit to things, then only amateur work is likely to be a good path. 
If "crumbles easily" means "cannot handle people challenging ideas", then leading investigations is definitely out, and any sort of doctoral program is likely problematic.  On the other hand, if it means "is easily hurt by verbal abuse" then graduate school is entirely possible---it would just be important to find a good advisor match and some sort of supportive personal network.