Are the colours meaningful in your app?
I would say having a limited set of colours is important whenever there is a meaning attached to them. The number of colours used, however, can be various. For example, you can have different colours used for:
- normal text
- a link
- a hovered
- a visited link
- an inactive link
- a primary button
- a secondary button
- a disabled button
- a hovered button
- some status: ok/done indicator
- another status for: wrong/error indicator
- another status indicator saying there is an ongoing operation
As you can see, even though there could be some unification provided, this list already contains 12 colours. Should you add a creative layer (different colours for some headers for example, or for some inverted elements like menu (here on UX.SE menu background is dark and the Ask Question button is sunflower yellow), some special elements (e.g. badges here on UX.SE again) – this number increases. However, if these are still meaningful, I see no problem with them.
Is your app all about colours?
Regarding the topic or the visual aspect of it, there are some apps that are strictly about colours, e.g. they contain colour swatches or refer to some colours of physical things (e.g. paints).
Are there colours that are similar?
As 80 feels to be a quite high number, you could check if there are some close colours used to support the same kind of elements. For example, links here and there can use different shades of blue, barely visible to the eye, but still different. In these cases, the frontend developer might consider going through them just for the sake of an audit and maintenance of the code, to provide a cleaner css.
Are there colours that are not important at all?
This refers to the importance of the colours. As 80 feels just a little bit suspicious, you could consider going through them to see if particular colours are not important – they just trigger concern, but do not drive Users to any results that would be valuable for them.