Theodore Roosevelt's cousin Franklin was the one who finally put it to bed, requiring a constitutional amendment.
But even without the amendment it is true. Here is a political cartoon from the time period illustrating.
Prior to progressivism, we had people and politicians moral enough to willingly step down in addition to rejecting such things, simply because it was the right thing to do. Now they all want to be tyrants. That's what 100+ years of progressivism will result in.
The whole purpose of your argument was that Roosevelt only felt "safe" in using Executive Orders because he wouldn't have to face another election.
But the exact opposite was true. Roosevelt felt that he could get by with the Executive Orders because he felt the people would support him over Congress.
And he was mostly right. Most of the issues he advanced with Executive Orders were extremely popular with the people which isn't surprising given that Roosevelt won by a mind-blowing 18.8% spread in 1904. His issues were so popular, that Taft (his hand picked successor) easily won over William Jennings Bryan in 1908 on the platform that he would continue Roosevelt's policies.
Roosevelt used Executive Orders far more than any President who preceded him, but he did so because he felt he had the public's support, not because he knew he wouldn't have to face them again.