The first statement makes sense to me that your premium would have to increase, when you renew your policy. When you renew, you will be x years older and therefore have higher mortality (ignoring the accident hump). If the cover amount stays the same, this makes the expected claim size higher, therefore the premiums need to be higher.
You have already undergone underwriting when you first took out your policy, so the insurer has some ideal of your mortality (even if underwriting was done 5 years ago). i.e They know you do not have hereditary diseases etc. They can therefore renew your policy without underwriting while still maintaining relatively small anti-selection risk. This offers the benefits of:
Decreased admin for insurer (setting up new policies and processing underwriting)
Decreased underwriting expenses (medical professionals are expensive)
Decrease in time wastage for client and better client experience
Increased business levels from clients renewing
They can therefore charge a smaller premium. The only risk is that the clients mortality drastically increased over the last x years and anti-selection from individuals who know they are sick choosing to renew the policy. This can be mitigated to an extent by requiring disclosure of any critical illness before renewal. Regardless, the anti-selection risk is likely to be outweighed by the cost savings from no underwriting.