You can replace '糖質源だ' with '糖質源になっている' without changing the meaning of the original sentence.
As Mobius Pizza is saying, sometimes '糖質源だ/糖質源である' are used instead of 'になっている'. Meanwhile, '糖質源です' and '糖質源になっている' are also objective and assertive expressions. Examples of subjective expressions are '糖質源だろう/糖質源でしょう'.
The 'has become...' sentence in Sjiveru's comment refers to the role of the rice in the past. But the original sentence only mentions the present state. The sentence in Sjiveru's comment
Rice has become an important source of carbohydrates in many diets
translates to, say,
As to PhoenixFox's comment, '糖質源になっている' and '糖質源だ' are both direct expressions. While the original sentence means 'It is 'usually' the case that...', the meaning 'usually' comes from '多くの食事で' (in many diets). If you say, omitting 'in many diets',
this is equal to saying
Therefore, you can replace '糖質源になっている' with '糖質源だ'.
However, as mentioned in the comments, 'になっている' seems to be more frequently used than 'だ'. The reason is unclear to me, but there is a similar, widely-used expression '...源になっている/...源になる'. Also, the author might prefer the rhythm (ending always with 'だ' makes sentences too short and monotonic).