A topic sentence that names two ideas gives the paragraph permission to wander between them, and the paragraph almost always takes it. “Public transport is cheaper and better for the environment” looks efficient and produces a paragraph that half-argues two things — which reads as a list, because it is one. Naming one idea forces every following sentence to answer to it, and that constraint is the whole point of the sentence.
The second requirement is that the claim be arguable. “Many people use public transport” is a fact, and a paragraph cannot develop a fact: there is nothing to support, so the sentences that follow can only add more facts. “Public transport is underfunded relative to its usage” is contestable, and everything after it has a job.
The third is that it belong to the essay. A topic sentence has to advance the thesis, not merely introduce a subject that is nearby — a paragraph that opens with a true, arguable claim your position does not need is a paragraph the examiner cannot connect to the answer.
Two ideas in the opening sentence produce a paragraph that argues neither properly.
If nobody could disagree, the paragraph has nothing to develop and can only add facts.
It has to move your position forward, not merely be about the same topic.
A claim that arrives in sentence four leaves the reader three sentences without knowing what the paragraph is for.
