Besides dim regularization, what are the advantages of Euclidean QFT?

It is very good question!

Besides some technical advances, that you already presented in question, first of all, very important to realise statement:

The Osterwalder-Schrader reconstruction theorem states that correla- tors in a reflection positive Euclidean QFT can be analytically continued to give Wightman functions that are tempered distributions on Minkowski space $R^{d−1,1}$.

See, for example, section 3 of Lorentzian methods in conformal field theory Slava Rychkov. Nowadays, these ideas extensively studied in CFT, see also this. Main idea is very illustrative:

Unitary Lorentzian CFTs are related to reflection-positive Euclidean CFTs by Wick rotation. This is the Osterwalder-Schrader reconstruction theorem. Thus, in principle, everything about a Lorentzian CFT is encoded in the usual CFT data (operator dimensions and OPE coefficients) that can be studied in Euclidean signature. However, many observables, and many constraints on CFT data are deeply hidden in the Euclidean correlators.

Also, it's very important to realise, that Euclidean QFT are used in condensed matter physics. For example, it is useful tool for describing of critical phenomena.For introduction, one can consult David Tong: Lectures on Statistical Field Theory.