It seems to me that languages with few phonemes tend to have more, and more extreme, allophones and free variation.
By “extreme”, I mean physically wider ranging. Obviously all languages have some allophony: in English for example /n/ can be alveolar, post-alveolar, or dental, depending on context.
However, this is low key compared to the allophony displayed by the languages with few phonemes. More specifically, those with few vowel phonemes show greater allophony in the vowels (and so for the consonants).
In Samoan, which has half a dozen consonant phonemes, /l/ can be [l] or [ɾ] depending on phonetic context. /t/ can be [k] or [t], and /n/ can be [n] or [ŋ].
In some dialects of Arrernte, (a language or dialect cluster spoken in Australia’s Northern Territory), there are 64 consonant phonemes but only 2 vowel phonemes. These are written as /a/ and /ə/, but that /ə/ can be anywhere from [ɪ] to [e] to [ə] to [ʊ], in free variation. (This is not considered allophony because the variation isn’t tied to phonetic context).
It seems as though even in the languages that are phonemically simplest, there is a tendency to fill the phonetic “space”.