You're quite right that pervasive is often used when describing the extent of something negative. Looking at pervasive in Oxford Living Dictionaries:
(especially of an unwelcome influence or physical effect)
spreading widely throughout an area or a group of people.
Looking at the first few example sentences in the same dictionary entry, let's decide for each if the thing pervasive refers to is positive 😊 , negative ☹ , or if it's hard to say [?] :
‘Ageism is pervasive and entrenched in our society.’ ☹
‘Knowledge networks have become pervasive because they can be simple
to implement.’ 😊 [?]
‘He exercised a pervasive influence on European drama by challenging
the conventions of naturalism.’ [?]
‘But it's the pervasive humour that wins through, thanks to a nicely
crafted script.’ 😊
‘Nevertheless, their influence is pervasive within the history of
‘It has become so pervasive that it influences how people write for
the Web.’ ☹ [?]
It's difficult to determine with sentences in isolation, but, roughly, out of six example sentences, one is definitely positive (and another, the first, very probably is), one is definitely negative (and another, the last, very probably is), and the other two sentences are difficult to classify as either negative or positive.
Not conclusive, it would seem, but that's good enough for us to be able to say:
Pervasive is often used with a negative slant (and may carry a presumption of negativity), but is also often used to describe positive effects without any difficulty at all.
Pervasive is fine in your context.