From 1974 until about 10 years ago, my house had a Weil-McLain electric boiler for the baseboard hot water heat. It drew about 120 amps if all four elements were energized, which happened in very cold weather. It was connected to its own 150 A main breaker, which had its own line (2/0 AL) coming from the meter. At the time of the boilers installation, the overhead service drop was replaced with heavy duty wiring with an ampacity of 400. In the 30+ years it was in service, never once did we have any issues with the breaker tripping. However, the first winter we had it, on a very cold day, we woke up in a cold house with no electric. The two houses across the street were also out. The power company replaced a fuse on the transformer, but it blew out again that evening. The next day they came back, and installed a new transformer just for our house. After that, no trouble associated with the electrical service. The boiler elements came on in stages, according to how much heat was required, so no huge load all at once. The voltage on the other circuits (in another panel) stayed stable, with very little drop even when boiler operating on all elements.
A premium quality panelboard, such as Eaton CH series or Square D QO series, have plated copper bus bars instead of aluminum as found on cheaper models. These panels and their breakers should not have any problems withstanding heavier load such as these tankless heaters, as long as panel is of the proper amp rating, and the associated wiring is properly installed.