make this statement better : Easy accessibility to healthcare should be a priority for the government in order to improve overall public health.
Here's a few variations on that statement that might be considered better:
 - Improving overall public health is an important goal, so governments should prioritize easy accessibility to healthcare.
 - If there isn't easy accessibility to healthcare, it will have a negative impact on overall public health.
 - Most people in society will at some point need healthcare. If it's easily accessible, this improves health outcomes for many of these people. The government can, and should, improve this accessibility as one of its priorities.
What is the logic behind easy accessibility to healthcare leading to improvement on overall public health?
The logic behind easy accessibility to healthcare leading to improvement in overall public health can be explained as follows:

- Access: When healthcare is easily accessible, more people can avail of medical services without facing barriers such as cost, distance, or long waiting times. This enables a larger portion of the population to address their health needs promptly.

- Prevention: With easier access to healthcare, people are more likely to engage in preventive measures such as vaccinations, regular check-ups, and screenings. This can help identify potential health issues early on, which can then be treated or managed more effectively.

- Education: Accessible healthcare often comes with increased health education, empowering individuals to make informed decisions about their own health and well-being. This may include understanding the importance of a healthy lifestyle, recognizing the signs and symptoms of common illnesses, and knowing when to seek medical care.

- Timely Treatment: When healthcare is accessible, people are more likely to seek treatment for illnesses or injuries in a timely manner. Early treatment often leads to better outcomes, as many conditions are more manageable or curable when caught early.

- Management of Chronic Conditions: Accessible healthcare enables better management of chronic diseases, as individuals with conditions such as diabetes or hypertension can receive ongoing care and monitoring. This can lead to improved health outcomes and a reduction in complications from poorly managed chronic illnesses.

- Mental Health: Easier access to healthcare services also includes mental health support, allowing people to seek help for mental health issues without barriers. This can lead to improved mental well-being and overall health for the population.

- Reduced Health Disparities: When healthcare is accessible to all, it helps reduce health disparities among different socioeconomic groups. This ensures that everyone, regardless of income or social status, has the opportunity to maintain and improve their health.

- Improved Public Health Outcomes: All of the above factors contribute to a healthier population with fewer incidences of preventable diseases, reduced morbidity and mortality rates, and better overall quality of life. This, in turn, leads to a more productive society and reduced burden on the healthcare system.