Any connecting wire contains inductance and this sets up a resonant circuit that can amplify noise. This is usually a high Q circuit. Your well-shielded transformer, when connected into the circuit, may increase the system noise. A line frequency isolation transformer usually does not protect for over voltage, sags, harmonics, or radio frequency interference. The shields can either help radio frequency interference or make it worse.
Isolation transformers are expensive compared to conventional transformers.
Samuel M. Goldwasser on his website has a low cost way of making an isolation transformer , he recommends using two similar transformers in series with the highest voltage secondaries connected together. For further reading see Morrison, R., Grounding and Shielding Techniques in Instrumentation , 3rd Edition, Wiley, 1986. This is the best book I know of on the subject and contains both a theoretical explanation and much practical advice on actually building shields into transformers. I had a tough time understanding shields and grounds until I studied this book. It gave me the tools I needed to solve many noise problems in systems powered by switching-mode power supply.