If Elizabeth hadn’t been heir to the throne and so popular, Mary would have had all she needed to execute her. Treason was in the eye of the beholder at the time. Elizabeth was known to have close associations with some of the leaders of the rebellions which took place during Mary’s reign, which was more than adequate reason for her to lose her head.
The Countess of Salsibury in Henry VIII’s reign was executed because of her close blood ties to the throne, and the fact that a religious garment was found in her house. This garment had also been used as the banner symbol for one of the rebellions that took place during Henry’s reign, and that was taken to be enough evidence to have her killed.
And if he didn’t have them, he’d make them up. Anne Boleyn was almost certainly not guilty of the charges against her. In fact, on some of the dates when she was supposedly commiting adultery in one palace, it can be proven that she was in another location alltogether, surrounded by people. (One of the dates was when she was recovering from childbirth.) Right before she was executed, the king’s marriage to Anne was annulled, so in essence, she was executed for adultery when she had never been married to the king.
Katheryn Howard was executed for adultery as well, but there’s no evidence she actually “soiled her sovereign’s bed.” She had been unchaste before her marriage-- that much she admitted, but she steadfastly maintained she had never cheated on Henry. Even under torture, the men with whom she was accused never admitted to anything beyond flirting. One finally confessed that she might have intended to sleep with him, so Henry had a law passed quickly that intending to commit adultery was treason, as was concealing your sexual history if the king expressed interest in marrying you. With this, Katheryn could be retroactively found guilty and killed.
She was not the first queen. The first was Queen Matilda, but that was a bad example because Matilda’s short reign ended in civil war.
Mary was powerless because she allowed herself to be powerless. . Mary capitulated to the notions that women needed a man to guide them and thus lost the love of her people by marrying a foreigner. (The English were very xenophobic at this time.) She allowed herself to be bullied.
Elizabeth was much smarter. She knew she could never marry. If she married a foreigner, she would lose the love of her people and be subject to her husband’s whims. If she married a subject, she could cause a civil war from jealous factions. She was intelligent enough not to let people know this, though, and up until her old age, she kept suitors dangling, gaining their favor and protection for England while she stretched out the process as long as possible. She played with the notion that she was an indecisive woman, using it to her advantage. She also knew how to keep her court in check and make sure the power stayed in her own hands instead of with her council.