Dangers.
If you are right in your self-diagnosis, the lack of an official Dx might prevent you from receiving appropriate assistance now or in the future. Even if you show few or no impairments now (and hence are really BAP rather than AS) that could change in old age, when a proper Dx might alert carers to your special needs (e.g. sensory sensitivity issues in aged care facilities?)
If you are wrong in your self-diagnosis, you may mistake the reasons for your behaviour and hence take inappropriate action (or inaction). A made-up and somewhat ludicrous example: if you think you lack social skills because you have diagnosed yourself with AS, when it is really a result of frequent drunkenness, then you may fail to deal with your alcohol problem. More subtle (and more likely) examples are when you really have other conditions where differential diagnosis with AS is complex (schizophrenia, bipolar, ADHD, social phobia, etc).
On the other hand
If you are my age (50s), and were about 40 years old when AS was introduced into DSM-IV, then you (a) necessarily missed out on a childhood or teenage diagnosis; (b) somehow got through the problems of growing up with AS and coped, maybe with intervention that did not need a diagnosis to be effective; (c) may not have any parents alive to inform a diagnostician about your childhood behaviour (which presents a problem for diagnosis, according to Simon Baron-Cohen); (d) do not need any intervention now (you have found a safe niche and are comfortable with your quiet, socially low-key life and are financially independent); and (e) do not imagine that getting a diagnosis (even if still possible) will help you much in old age. If these conditions are true, self-diagnosis - particularly by someone reasonably knowledgeable about psychology and about doing their own research - may be a pleasant and insightful hobby. It may be a relief, a change of self-understanding, without requiring a change of life.
Also, a formal diagnosis could lead to all sorts of changes - either in how other people (and even organisations, such as health funds) regard you, and in how you regard yourself. While you have some control over the latter, you cannot control the reactions of other people or organisations. You could end up losing some or all health cover, for example, or suffer career problems - e.g. discrimination. So there are some risks in getting a Dx.
I tend to think that some self-diagnosis is necessary - at least for someone my age - because you would not fork out large sums of money to get a reputable psychological assessment by professionals skilled in AS unless you thought AS was already a strong possibility, indeed a "most likely hypothesis" that you seriously wanted to verify or falsify. So the issue is not "self-diagnosis" but whether it is going to be worthwhile progressing beyond the existing self-diagnosis to get a formal assessment as well. And that will depend a lot on circumstances, I think.