With the abdication and accession, surveys have been polling nationally representative samples of voters about their attitudes towards the monarchy.
The evidence of the surveys is that very few voters' views match those of ultranationalists who would restore political power to the monarchy or republicans who would abolish the imperial system.
Summary:
74% in the Mainichi Shimbun survey, 78% in the Yomiuri Shimbun survey, and 80.9% in the Kyodo News survey back the
current system, in which the emperor is defined as the "symbol of the state", without having political powers.
4.8% in the Kyodo News survey, 7% in the Mainichi Shimbun survey, and 7% in the Yomiuri Shimbun survey want to
abolish the monarchy.
4% in the Mainichi Shimbun survey, 4.3% in the Kyodo News survey, and 5% in the Yomiuri Shimbun survey want to give the emperor
more power.
7.3% in the Kyodo News survey said the emperor should be considered a sacred figure. The question apparently wasn't included in the other surveys.
See the full results and more survey questions here.
Over 82% feel affection for new emperor, 79% support woman on throne
74% back emperor as symbol of state defined by current Constitution: Mainichi poll - The Mainichi
78% support symbolic emperor system - The Japan News
The results also show why the traditionalists and nationalists are not pressed to address concerns about the line of succession running out. With so few republicans, the monarchy will clearly continue even if the current imperial family dies out.