How do you secure the network if you cap the coin?  How many new successful coins are capped these days?  

In the short run Bitcoin & Litecoin has a higher supply inflation rate that Doge.
             Dogecoin  Bitcoin    Litecoin
  2015   5.26%     10%       33.33%
  2016   5%          9.09%    12.5%
  2017   4.76%     4.1%      11.11%
  2018   4.54%     4%         10%
  2019   4.35%     3.85%    9.09%
  2020   4.2%        3.7%      4.1%