I disagree it is not the path of renouncing sense objects, but the path of renouncing attachment to sense objects. If they renounce sense objects, they would not be eating and drinking.
Exactly, we have to understand what the spang bya (སྤང་བྱ་) is, the object of abandonment. It is not the sense object themselves but the attachment and other delusions that arise connected with those sense objects.
The thing is, as our understanding of emptiness increases we can apply it to our experience of different objects, including the ones that cause our attachment and aversion. For example, if we can see our enemy as a dependent arising, or something merely designated, then already this will greatly decrease our experience of anger or aversion when we encounter them. Similarly, it will allow us to reduce our attachment to pleasant objects. Before that realization, Chandrakirti and other masters advise maintaining distance, or space, between oneself and the object of attachment/aversion.
We can apply emptiness right from the get go. However, the realization of emptiness itself requires a vast collection of merit and sharp faculties. If we wish to be able to develop this emptiness to the level of a complete realization, a vast accumulation of merit is required. If we want that realization of emptiness to lead to full enlightenment, we need to develop compassion and bodhicitta along with it. In order to build up compassion and bodhicitta, we need to be willing to train in generosity for example to get rid miserliness and its imprints, as well as cultivate patience because without patience one will experience endless obstacles in trying to benefit other sentient beings, who are difficult to tame.
In the teachings on developing concentration/shamatha, the texts speak of developing two factors, little desire ('dod chung འདོད་ཆུང) and contentment (chog shes ཆོག་ཤེས). Actually these two attitudes are aimed at developing enough renunciation to be able to maintain the seclusion and simple lifestyle necessary for developing concentration. As we know, a complete penetration of emptiness is not possible without developed concentration. So I would say that I agree that some renunciation of the sense objects is necessary, but more importantly is a renunciation of the attitude of attachment associated with them. Without the attachment to the sense objects it is possible to be surrounded by them and still progress on the path- as we see with some of the great bodhisattva kings in Mahayana literature.