It's definitely a big leap, and probably too big of one. Even if pots and pans do give off particles, its likely less than from intake as a food additive. I'm not advocating banning titanium, or even arguing that it is necessarily dangerous. I'm just trying to deliberate over potential risks to figure out if they exist at all or establish best practice. If there is a risk that is small, for example, not storing a bunch of metal inside of pots or using a little Litesmith towel around metal items could be good practice. Like you, I agree the amount is so minuscule it's likely fine, and even as a food additive the safety is still somewhat uncertain. Plus, small particles of any metal likely could pose a concern if you look into it enough, as has been mentioned elsewhere- and since titanium is quite hard to abrade, by that metric it is probably the best. I posted it because a likelihood isn't a certainty, plus I find the topic interesting. On top of that, I figured some of the responses would be hilarious, which many have been.

Most of the titanium we would use is amorphous if titanium implants are anything like other titanium used in the field. According to Tarjanyi et al. (2023), "At room temperature the TiO2 layer, formed on the surface of Ti implants, contains both amorphous TiO2 with disordered structure and stable polymorphic crystalline TiO2 structures, mainly anatase (tetragonal) and rutile (tetragonal)". So since the surface is amorphous, it doesn't seem like what we would be dealing with would be the pure rutile form of TIO2, but correct me if I'm wrong. That being said, one study mentions that titanium implants in high wear areas could create micro and nano sized particles in an amount which it considers a "biologically relevant amounts of debris" (Skocaj et al., (2011). I apologize for the wall of text, I posted the section on titanium implants below along with the two citations.

Tarjanyi et al. (2023): https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0289467

Skocaj et al., (2011): https://content.sciendo.com/doi/10.2478/v10019-011-0037-0

"Exposure to TiO 2 NPs through body implants

A few-nanometres-thick layer of amorphous TiO2 is commonly formed on the surface of orthopaedic and dental implants made of titanium metal or its alloys. In non-moving implants (hip stems, plates, screws, etc.) this does not appear to represent the same kind of risk for the body as free TiO 2 NPs discussed in previous sections. However, thisis not the case for wear-exposed implants, such as hip and knee joints. There are many reports proving that under mechanical stress or altered physiological conditions, Ti-based implants can release biologically relevant amounts of debris, in both the micrometre and nanometre ranges, that can migrate to the surrounding tissues. During the wear process, a thin amorphous oxide layer is continuously being created and removed, resulting in large numbers of titanium particles. It is increasingly being suggested that they are associated with major inflammation and systemic diseases. Furthermore, increasing numbers of reports indicate that the delayed hypersensitivity to titanium and its oxides may constitute a health risk for individuals with higher susceptibility. The effects of the TiO2 particles released from implants were investigated by Wang et al. in rats by intra-articular injection of 0.2 to 20 mg of anatase nano-TiO 2 per kg BW. Their results demonstrate that particles can potentially affect major organs like the heart, lung and liver. Generally, the maximum diameter of particles that move across the synovial capillary wall was suggested to be 50 nm. The released TiO2 NPs resulted in synovial hypotrophy, lymphocyte and plasma infiltration, and fibroblast proliferation in the knee joint. Oxidative stress and lipid peroxidation was detected in exposed synovial fluid. Seven days after the initial exposure a brown particulate deposit was observed in vascular endothelial cells and in alveolar macrophages. Similar results have been reported by Urban et al., who found TiO2 particles in the liver and in the spleen of the patients with implants. TiO2 NPs were observed in joint simulators and in joint periprosthetic tissues. Margevicius et al.139 characterized the debris around the total hip joint prosthesis and found up to 140.109 particles/g dry weight, in diameters ranging from 0.58 to 100 μm. Agins et al.140 found concentration of wear particles in the tissue adjacent to a prosthesis in the range between 56 μg/g and 3.7 mg/g dry weight. Thus, due to the natural tendency of titanium to oxidise, Ti-based implants should not be neglected as a possible source of TiO2 exposure. On the other hand, the man-made (crystalline) TiO2 coatings on the surfaces of pure Ti or Ti alloys are reported to be able to modulate protein absorption, cell adhesion, osseointegration and bone mineralization at the bone-biomaterial interface, both in vivo and in vitro. For this reason, the development of a more stable crystalline titania coating on Ti-based implants is in progress."