I think there's been a bit of a miscommunication here?
Most children with SLI will have semantic and pragmatic issues as language is the core issue.
If you think of language as being
syntax
semantics
pragmatics
fluency
then any child with a significant language impairment is likely to have difficulties in most domains.
This means that there are children with pervasive language impairments who have semantic and pragmatic issues who do not have ASD - their semantic and pragmatic issues are part of an overall language impairment. They may appear socially different or "odd", they may have all sorts of self-stimulatory behaviours going on, they may withdraw from social contact etc but these behavioural symptoms, if you like, relate primarily to a linguistic deficit.
Children with what is commonly referred to as an SPD may have language and IQ features in common with these children, but they typically have advanced vocabulary that they don't know how to use very well in context e.g. they can have severe communication difficulties, but good surface language skills. The current belief is that these language features stem from an underlying autistic-type difficulty.
It may help to think of it with reference to the adult population who have acquired language difficulties e.g. after brain trauma or stroke?
There are individuals with right hemisphere damage after stroke or traumatic brain injury who are very precise in terms of language use, very literal, good vocabulary but poor communication etc, can use language apparently fluently but with little context, what they say isn't relevant etc.
There are individuals with left hemisphere damage after stroke or traumatic brain injury who can formulate an idea but not really translate it into words. They struggle with sentence formation and word-finding and getting the content of their message across.
Both have severe communication difficulties. It's not a question of which is "better" or which is "worse" - they are different and there is a different underlying neurological reason for their language difficulties.
This is a crude representation of different language and communication difficulties - in reality in adults, as in children, each person can present slightly differently. Children more so than adults as they have a dynamic and developing language system and we can't really draw conclusions from the adult population: but I include the example to give an idea that there are recognised and proven differences between communication impairments (by fMRI etc), it's not all just a matter of who decides what label "fits" subjectively.
So, I do have to support the idea that SLI can be a lifelong pervasive disability in this discussion. I work with high school students with SLI and with ASD and yes, there is overlap.. but there are also differences. There are some students who would be best placed in an SLI setting with intervention focused more on the linguistic impairment and some in an ASD setting with intervention focused more on the social impact of the linguistic impairment. Both groups of students need language and communication intervention, but there are subtle differences in how to address these, with students who are more HFA tending to need a lot more support with emotional regulation than SLI students etc.
Crucially, I do believe that across the two settings in which I work, there are some students with ASD who are less disabled than some students with SLI, some students with SLI who are less students than some students with ASD etc. The label doesn't really define the level of difficulty that each individual student has..
Unfortunately, we have a situation in this country where SLI is extremely poorly understood and extremely poorly resourced. So it will be true that in some areas, the label that a child has will either open doors to intervention or shut them. However, that is not the case in all areas. In mine, it is actually quite likely that there might be more support for a student with SLI and a student with HFA than, say, a student with moderate autism. Postcode lottery...
Here is a link about the issues around recognition of SLI by one of the country's major experts in the area