Paracontrolled calculus was developed by Gubinelli, Imkeller and Perkowski as a way of treating singular stochastic PDEs such as KPZ, $\Phi_3^4$ or PAM, around the same time regularity structures were introduced by Hairer.
Regularity structures are now the standard treatment of singular stochastic PDEs although I have been reading that there are perhaps potentional benefits to paracontrolled calculus. This paper for example says:
We develop in this work a general version of paracontrolled calculus that allows to treat analytically within this paradigm some singular partial differential equations with the same efficiency as regularity structures, with the benefit that there is no need to introduce the algebraic apparatus inherent to the latter theory.
I'm not sure that this is such a large benefit. Is this the only reason to work with paracontrolled calculus, or are there other benefits? Is there anything you can do in paracontrolled calculus that you can't in regularity structures?