None of these issues have anything to do with tank vs tankless. The water is hot (all heaters can be set hotter than 120F) at the source, after that it is all plumbing.
Actually, that's not quite correct (based on analyzing a few systems.)
1. I've not yet been in any houses with tankless water heaters where the owners knew the temp could be set higher than 120, let alone how to do it--unscrewing the cabinet and changing a jumper in a Rinnai for example. I've done it myself in two houses now.
2. Tankless units perform poorly on intermittent draws (HE washers, rinsing periodically while handwashing dishes, etc.) because the heater kicks out creating cold water sandwiches. Tanks have much less problem with this, particularly if the lines are insulated.
3. Tankless units have a start up lag before any distribution losses. I've measured the lag time before hot water can be felt at the copper discharge line of our tankless--heating can be sensed at 15-18 seconds with an approximately 1.6 gpm hot water draw (measured vs. 1.5 gpm nominal.) A tank doesn't have an appreciable delay directly at its discharge.
4. All of the larger newer homes I've seen with tankless have had some sort of Manabloc system with PEX dedicated runs which is advertised as reducing lag time, but seem to have the opposite effect as installed. I measured the present one as having roughly 22 feet of 1" PEX from exterior wall to ceiling and around corner of nearby garage interior Manabloc installation. With a 1.6 gpm draw and length of Manabloc added this worked out to about 27 secs before the dedicated line to the kitchen faucet is even factored in. Combined lag with tankless heater was roughly 45 secs, so even the shortest runs in the home take a long time to reach temp. Measurement confirmed the calculated lag to within 1 sec.
5. The dedicated lines in newer installs are also dubious solutions in some instances. New homes often have a dedicated kitchen sink and dedicated dishwasher line, and are often the longest runs in the house. Sharing a line of the same size line is a better idea because otherwise the dishwasher will get a long slug of cold water before any hot enters, even if the supply to the Manabloc is already hot. The kitchen run in our newer home is ~99 feet of 1/2" PEX (up into attic, across & around furnace/attic entrance and back down wall.) This is 0.91 gals of water and ~34 secs of additional lag.
In the above total lag time at the kitchen sink works out to 1 min 19 secs calculated, while I measured an actual lag of 1 min 30 secs. Reaching temp took even more time, but was much less of an issue at 130 F set point for the heater.
These delays are only partially the fault of the tankless heater. The Manabloc systems don't appear to have been optimized in any install I've yet seen. Ironically, the systems are often sized for higher flows than they are likely to be subjected to. Additionally, newer faucets in the kitchen are designed for 1.5 gpm (mine is running a little higher as illustrated above) vs. 2.2 gpm prior standard. This results in a greater observed lag because the same volume of water must still be displaced in the distribution line.