Although general not done for special expensive exhibits, most museums with substantial admission fees offer free days or free nights.  I am sure that this was implemented in part due to the very concerns you express.  When I worked at small museums we would discretionarily waive fees and had a special family rate. Desk clerks do not always have the authority to do this.  BTW Your paid admission ticket buys you convenience and fewer patrons.
 
Don't think I'm unsympathetic. I'm a well-known cheap skate, still in shock from the idea that it costs $40 to get someone to mow my lawn today.
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