I don't think the concern over pinging 1.1.1.1 is warranted.
ICMP is pretty raw Network traffic, meaning you're not really causing much actual load here.
You can't even really try to DDOS with normal ICMP packets. You usually have have to max it's size out at 64KB with an ICMP floor to even think of having an effect. Vs the, effectively inconsequential, 32 bytes of a normal ICMP packet.
You watching a short YouTube video is equivalent Network load as 180 days of pinging for Network up time.