Again, this is not true.^ Have you tried this? Again we did this only far more extreme in giving away a free month of mowing. If you sell it as hey I will cut your lawn for $10 for you to try it out and see from there then yes you may end up in the situations you explain.
If you do go that route then yes you have a poor thought out plan. If you use this to get customers to call and get started then up sell and sign them up for early service this is an easy win.
If I give away my first mowing for $10 and sell the customer on $36 a week mowing for the summer, you now sell full price mowing for $35 a week who wins? Who had an incentive for the customer to call to begin with? Which one do you think has more people calling asking questions about other services you may offer?